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Research in economics and game theory. A 70th anniversary
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Research in Economics and Game Theory. A 70th Anniversary Federico Etro PII: DOI: Reference:
S1090-9443(17)30037-6 10.1016/j.rie.2017.02.001 YREEC 708
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Research in Economics
Please cite this article as: Federico Etro , Research in Economics and Game Theory. A 70th Anniversary, Research in Economics (2017), doi: 10.1016/j.rie.2017.02.001
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Research in Economics and Game Theory. A 70th Anniversary
Federico Etro
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Editor in Chief of Research in Economics Department of Economics, Ca’ Foscari University, Italy
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This Special Issue of Research in Economics dedicated to Game Theory coincides with the 70th anniversary of the first issue of our journal, born indeed in 1947. We are delighted to celebrate this anniversary announcing that we have reached 300 submissions over the last year and announcing an important renovation of our Editorial Board. We welcome as new Coeditor Steve Levitt from the Department of Economics of the University of Chicago, one of the most brilliant empirical economists of the last decades and a recipient of the John Bates Clark Medal in 2003: his wide knowledge on applied economics represents a fundamental contribution for our journal. We are also pleased to welcome, as Co-editor, Paolo Bertoletti from the University of Pavia, an experienced microeconomist whose critical acumen represents a major addition to the editorial activity of the Board. Together with them a few exceptional economists have joined our Board as Associate Editors: Manuel Arellano (CEMFI, Spain), Claude d'Aspremont (Université Catholique de Louvain, Belgium), Robin Boadway (Queen׳s University, Canada), George Borjas (Harvard University, USA), Hong Bin Cai (Peking University, China), Andrea Colciago (Dutch National Bank, Netherlands), Ravi Kanbur (Cornell University, USA), Silvia Marchesi (University of Milan, Bicocca, Italy), Toshihiro Matsumura (University of Tokyo, Japan), Pierre Perron (Boston University, USA), Hashem Pesaran (University of Southern California, USA), Pierre Pestieau (CREPP, Université de Liège, Belgium), Assaf Razin (Tel-Aviv University, Israel), Harvey Rosen (Princeton University, USA) and Kenneth West (University of WisconsinMadison, USA). We are grateful to all of them for accepting these positions and to the past Coeditor Alberto Bisin and the past members of the Editorial Board who have completed their service with this issue. ***
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The following pages will introduce this Anniversary issue on game theory relating its articles to the general development of this field of applied math. As well known, game theory studies strategic interactions between decision-makers who maximize their expected payoffs. It was moving its first steps 70 years ago, just like our journal. Indeed, expected utility theory was founded on basic axioms of rational preferences in the Appendix to the 1947 Edition of the monumental book of John von Neumann and Oscar Morgenstern, “Theory of Games and Economic Behavior”, and provided the definitive microfoundation of standard economic models of rational behavior under uncertainty. Most of all, that book introduced the first comprehensive treatment of basic game theory, with a special focus on zero-sum games, which are basic games where the net gains of the players are null (as in Stone, Paper, Scissors), but also with the more ambitious aim of building a new approach to economic theory based on equilibrium interactions between a small number of rational players.
Email: [email protected].
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The next crucial step in the development of a formal theory of games was the definition and the characterization of an equilibrium concept. Nash (1950a, 1951) defined the notion of a non-cooperative equilibrium where the strategy of each player is the best response to the strategies of the other players, and proved existence of this equilibrium in mixed strategies (as in Stone, Paper, Scissors, where each player should randomize between the three options with equal probabilities): this is what we now call a Nash Equilibrium, which is regularly applied to static games where players act simultaneously (such as competition in quantities or in prices). Nash (1950b, 1953) introduced also a cooperative equilibrium concept for bargaining games and derived its axiomatic foundation.1 Selten (1965) refined the Nash equilibrium to the notion of SubGame Perfect Equilibrium, which is based on the fundamental principle of backward induction (in practice: first, understand what will happen tomorrow as a consequence of today’s choices, and, then, you can figure out what is your best choice for today) and is now the standard equilibrium concept for games with perfect information and multiple stages (such as leader-followers’ games or spatial games of location and pricing).2 Harsanyi (1967) introduced the Bayesian Equilibrium for games with incomplete information, where players maximize their expected utility under incomplete information and given the beliefs about each player’ type: later the concept was refined allowing agents to update their beliefs over time according to the Bayes’ rule on the equilibrium path and, in the Sequential Equilibrium developed by Kreps and Wilson (1982a), also off the equilibrium path.3 The last decades have seen an explosion of applications of game theory and new equilibrium concepts in virtually any field of economics as well as other social and natural sciences.4 Excellent textbook treatments can be found in Fudenberg and Tirole (1991), Myerson (1997) and Rasmusen (2006). The prisoner’s dilemma is probably the most famous non-cooperative game: each of two prisoners can either confess that the other committed a crime or cooperate by remaining silent, and they will serve 2 years each in prison if they both confess, 1 year if they are both silent and respectively 3 and 0 years if a prisoner is silent and the other does confess. The game, whose unique Nash equilibrium is (confess, confess), exemplifies why strategic interactions may generate inefficient results and makes us wonder whether and how players can reach better outcomes. This issue is fundamental to understand not only rational behavior of agents in the economy, but also the development of institutions and social behavior sustaining cooperation. Deep down, any interaction can be seen as a game, indeed as part of the “game of life”, and the outcome of any game depends at the end on its future consequences. In a series of celebrated contributions, the political scientist Axelrod (1980, 1981, 1984) has analyzed experimental foundations for cooperation based on a so-called “TIT-FOR-TAT” strategy in a finitely repeated prisoner’s dilemma. Such a strategy, which requires one to cooperate on the first move and then to reciprocate by doing whatever the other player did on the previous move, won the tournament organized by Axelrod between a variety of different strategies, suggesting that reciprocity is not only a social norm, but also a successful rule for selfish agents. Kreps et al. (1982) complemented these findings with a theoretical foundation for reciprocity based on the same TIT-FOR-TAT strategy, and started a fruitful literature of interdisciplinary investigations on the role of information in social interactions. After 35 years, Robert Axelrod opens our Anniversary Issue with a new Another important solution concept in cooperative game theory with a variety of applications is in Shapley (1953). 2 The classic work on bargaining games in a dynamic framework is by Rubinstein (1982). 3 Important works on bargaining games under incomplete information are by Chatterjee and Samuelson (1983), Myerson and Satterthwaite (1983) and Mailath and Postlewaite (1990). 4 Other equilibrium concepts include the Correlated Equilibrium (Aumann, 1974), the Coalition-Proof Equilibrium (Bernheim, Peleg and Whinston, 1987) and Renegotiation-Proof Equilibrium, the Markov Perfect Equilibrium (Maskin and Tirole, 1988) and the Self-Confirming Equilibrium (Fudenberg and Levine, 1993). 1
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interdisciplinary essay written with Larissa Forster on “How historical analogies in newspapers of five countries make sense of major events: 9/11, Mumbai and Tahrir Square”. This is the first quantitative analysis comparing historical analogies invoked in three major events of this century within newspapers from five countries, and it will be certainly a valuable contribution to our understanding of salience, framing of information and rhetoric in decision making. The battle of sexes is another famous game where members of a couple chose separately whether to go to the opera or to a sport match, with symmetric positive payoffs if they chose the same event and zero payoffs otherwise: this is a game in which multiple equilibria emerge. Entry games are another example: when entry of a certain number of identical firms in a market is endogenous, different combinations of entrants could emerge in a simultaneous entry game, even if their identity is inconsequential for the nature of the endogenous market structure. However multiple equilibria can be genuinely different in other contexts. Consider publications in an academic journal: this is considered a good journal if top researchers chose to submit relevant articles to it, but top researchers chose to submit there if the journal is considered a good one, which allows for both bad and good submission equilibria in the absence of some coordinating device. The analysis of coordination through cheap talk in pre-play communication was introduced in a pioneering work of Crawford and Sobel (1982),5 and is crucial for understanding which equilibria should emerge and how preplay communication and its metastructure (based on thinking, a common language, rethoric, unwritten rules, written laws and even the informal “authority” of some players) can induce coordinated beliefs in specific games or in the same “game of life”. Such a foundational analysis underlies the essays of Vincent Crawford (“Let’s talk it over: coordination via preplay communication with level-k thinking”) and of George Mailath, Stephen Morris and Andrew Postlewaite (“Laws and authority”). Crawford adopts a structural non-equilibrium model based on strategic thinking to analyze coordination in a battle of sexes, showing that communication helps coordination and, with moderate differences in preferences, the level-k coordination rate6 is likely to be higher than the mixed strategy equilibrium rate even without communication. Mailath, Morris and Postlewaite move to the analysis of social conventions and institutions and acknowledge that endorsing executive decisions, passing legislation or announcing court opinions are just symbolic actions that make no real change in the “game of life” unless they help to coordinate the beliefs of citizens on the effects of the law and therefore their behavior. Since only a theory of cheap talk in coordination games can be relevant to understand laws and authority, these authors develop a related theory on how and when individuals have, gain and lose authority. Game theory has been widely employed to analyze politics and social choice, from the first application of the Hotelling model to two-party electoral competition to the application of mechanism design in the vain attempt of constructing ideal social choice functions (Gibbard, 1973; Satterthwaite, 1975; Peleg, 1978). Bezalel Peleg and Hans Peters build on this last tradition their discussion on “Feasible elimination procedures in social choice: an axiomatic characterization”, which founds social choice functions resulting from a feasible elimination procedure (which in practice requires voters to report complete preferences over alternatives) on the axioms of anonymity, Maskin’s monotonicity and independent blocking. The authors argue also that this axiomatic characterization can be seen as an extension of the majority rule for two alternatives (May, 1952) to a choice rule for at least three alternatives in On preplay communication see also Farrell (1987) and Crawford (1998, 2003). On the aggregate implications of coordination games see Cooper (1999), the important applications of Diamond and Dybvig (1983) and Morris and Shin (1998, 2002) and the recent work of Morris (2014). 6 The definition of level-k thinking is recursive: A level-k player adopts the best response to level k-1 players, with level-0 players acting randomly. 5
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a direct democracy. The essay on “Strategic dissent in the Hotelling-Downs model with sequential entry and private information” by Siddhartha Bandyopadhyay, Manaswini Bhalla, Kalyan Chatterjee and Jaideep Roy extends the classic model of electoral competition in a representative democracy to sequential entry of multiple office-seeking candidates with privately known qualities: the authors show that high-quality politicians signal their type adopting extreme ideological platforms compared to the median voter (while low-quality politicians randomize between mis-signaling quality and staying out of competition), which provides a new rationale for political polarization. Finally, the interaction of executive, legislative and judicial branches is the focus of the analysis of Jonathan Hamilton and Steven Slutsky (“Judicial review and the power of the executive and legislative branches”), which builds on their earlier design of efficient redistributive schemes in the presence of asymmetric information (Brito, Hamilton, Slutsky and Stiglitz, 1990).7 Both these two essays adopt the sequential equilibrium as their equilibrium concept. The development of behavioral game theory is one of the most interesting recent developments in theoretical and experimental research.8 For instance, it is well known that the strict logic of equilibrium and backward induction is often in contradiction with the way agents manage to commit to strategies in real life and in experimental situations.9 This emerges not only in finitely repeated prisoner’s dilemma games, but also in other dynamic games such as in the “Chain Store” game of Selten (1978) about entry deterrence of a sequence of competitors and in a variety of public goods’ games, where agents tend to contribute much more in experiments compared to the level of free-riding implied by a Nash equilibrium (see, for instance, Henrich et al., 2001). Imperfect information on the type of other players can help solving some of these paradoxes, as shown by Kreps et al. (1982) for the repeated prisoner’s dilemma and by Kreps and Wilson (1982b) for the chain store paradox. However, it is insufficient to explain what appears as a genuinely social behavior in other games, such as public good’s games or the “ultimatum game”, where an agent proposes how to split a prize and then a responder can either accept this or throw away the prize. Following the recent literature on behavioral game theory, Friedel Bolle has addressed this difficulty adopting social preferences based on inequality aversion (Fehr and Schmidt, 1999) or altruism and fairness (Rabin, 1993). His experiment tests these preferences in the “Passing the Buck” game, a new interesting dynamic game where multiple members of a group decide sequentially whether or not to incur costs so that they can fix a certain problem for the benefit of the group. The predicted unique Perfect Bayesian Equilibrium with incomplete information on the social preferences of the other players generally fits the experimental results. The analysis of strategic commitments in market competition is a traditional field of application of game theory to economics. Classic results have been derived within three classes of models that are now at the basis of the theory of duopoly. These were developed in the works of Dixit (1979) on quantity commitments by a Stackelberg leader, d’Aspremont, Gabszewicz and Thisse (1979) on location strategies with subsequent price competition between two firms, and Gabszewicz and Thisse (1979) on price competition between two firms producing vertically differentiated products.10 In this issue we present three essays that generalize these fundamental two-stage games.11 The Stackelberg game of quantity For further analysis of game-theoretic models of political science see the Special Issue on Political Economy of Research in Economics in September 2015 and, for an application to the political economy of international unions coordinating environmental policy, see Weitzman (2017). 8 For a comprehensive account of the literature we refer to Camerer (2003) and to Crawford, Costa-Gomes and Iriberri (2013) on strategic thinking, which is also the subject of the essay of Crawford in this volume. 9 For classic interdisciplinary applications see Schelling (1980). 10 Qualities of the two products were endogenized only later (see Choi and Shin, 1992). 11 For further analysis of game-theoretic models of strategic interactions see the Special Issue on Industrial Organization of Research in Economics in December 2016. 7
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competition with exogenous and endogenous entry is generalized by Antonio Tesoriere in “Stackelberg equilibrium with many leaders and followers. The case of zero fixed costs”: using lattice theoretical methods, the author provides a set of conditions for the existence of an equilibrium in pure strategies and characterizes nature and comparative statics of the equilibrium market structure when there are no entry costs. The Hotelling game is generalized by Jeroen Hinloopen and Stephen Martin in “Costly location in Hotelling duopoly”, which derives a set of conditions for the existence of an equilibrium in pure strategies and characterizes nature and comparative statics of the equilibrium locations. Finally, the Gabszewicz-Thisse model is generalized by Jean Gabszewicz, Marco Marini and Ornella Tarola in “Vertical differentiation and collusion: pruning or proliferation?”, where the authors characterize equilibrium qualities and prices in the presence of multiproduct firms. A supergame is an infinitely repeated game where cooperation can be sustainable as a SubGame Perfect Equilibrium as long as the players are patient enough, even if cooperation is not an equilibrium of the one-shot game. For instance, in the Prisoner’s Dilemma this happens with a so-called “grim trigger” strategy, which requires one to cooperate on the first move and then as long as cooperation takes place, but revert to the static Nash equilibrium strategy forever after a defection. More general treatments of such a Folk Theorem (a label due to the fact that the basic idea circulated between game theorists before being published) can be found in the works of Fudenberg and Maskin (1986) and Abreu (1988) which exploit the recursive nature of these games adopting punishments for deviators that minmax their payoffs, with a sort of “stick and carrot” structure. The literature has then derived a variety of Folk Theorems for supergames with short-lived players (Fudenberg, Kreps and Maskin, 1990), imperfect monitoring of actions (Abreu, Pearce and Stacchetti, 1990), random matching of players (Kandori, 1992, Ellison, 1994), private monitoring and any possible combination of these complications, culminating in the nice book of Mailath and Samuelson (2006).12 For interesting applications of models with random matching we recommend the works of Milgrom, North and Weingast (1990) and Greif, Milgrom and Weingast (1994) on cooperation in Medieval trade relationships. However, the main economic application of the theory of supergames is in the analysis of price-fixing cartels, where firms share a tacit understanding to raise prices. This form of collusion has been studied under noisy prices (Green and Porter, 1984), demand uncertainty (Haltiwanger and Harrington, 1991), private information on costs (Athey and Bagwell, 2001) and other extensions, characterizing when collusion is sustainable and at which prices. Instead, little is known about the type and strength of the mutual beliefs that can result in coordination and about the dynamic process that can lead from competitive to supracompetitive prices. On this topic we present an important work by Joseph Harrington Jr., “A Theory of collusion with partial mutual understanding”. Building on the concept of rationalizability in supergames with incomplete information, introduced in our journal by Battigalli (2003), the author provides a new foundation for paths toward tacit collusion based on mutual beliefs. Firms are assumed to commonly believe that price increases will be at least matched by the other firms, but lack any shared understanding about which firm will be the price leader, when this will increase its price and at which level: nevertheless, Harrington derives sufficient conditions for the emergence of supracompetitive prices and shows that these are bounded below the maximal equilibrium price. On the related literature on learning in games and evolutionary games see, inter alia, Kandori, Mailath and Rob (1993), Ellison (2000), Ellison and Fudenberg (2000) and the book of Fudenberg and Levine (1998). For an application of evolutionary theory to a compliance game see Petrohilos-Andrianos and Xepapadeas (2017). A somewhat related line of research in dynamic game theory, started by Isaacs (1954), concerns differential games in continuous time (for applications recently published in our journal see Itaya and Ursprung, 2016 and Kováč and Žigić, 2016). 12
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Building a reputation in repeated games has been the focus of a variety of theoretical investigations, from the model of Klein and Leffler (1981), where the expectation of repeat purchases of high quality experience goods at a price premium provides the incentives to deliver high quality, to models à la Kreps et al. (1982) where reputation to act in a virtuous way is built through persistent imitation of a committed type of player, to the more recent model of Mailath and Samuelson (2001) where reputation is built by exerting effort to benefit from separation in the market from an uncommitted type of player (for an interesting application to reputation building of artists in Renaissance Florence see O’Malley, 2013). An interesting review of the different theoretical approaches trying to capture the idea of reputation can be found in the book of Mailath and Samuelson (2006). In our volume, Eric Rasmusen builds on the Klein-Leffler approach to develop “A model of trust in quality and North-South trade”. This essay explains trade between identical countries in a general equilibrium framework where a country exports experience goods of high quality and high price whose reputation is sustainable in the long run, and imports cheaper low quality goods from another country. In line with modern trade theories, the analysis accounts for equilibrium in each national labor market and endogenous entry of high quality firms through investments in a non-price dimension.13 The analysis of mechanism design through the principle of incentive compatibility (Hurwicz, 1973) has been a fertile territory to exploit game theoretic analysis. The first application to a market setting has been to auctions (Vickrey, 1961), whose design has been studied in a variety of contexts, from complete information (Hillman and Riley, 1989)14 to incomplete information (Myerson, 1981, Riley and Samuelson, 1981, Milgrom and Weber, 1982), and in extensions with endogenous quantities (Hansen, 1988), common values (Bulow, Huang and Klemperer, 1999), asymmetries (Maskin and Riley, 2000) and multidimensionality (Athey and Levin, 2001; Athey and Ellison, 2011). The same principles of mechanism design under incomplete information have been applied to many other fields, including social choice and provision of public goods (d'Aspremont and Gérard-Varet, 1979; Ledyard and Palfrey, 1999), war of attritions (Bulow and Klemperer, 1999), optimal non-linear taxation and principal-agent contracts where the productivity of agents exerting effort is private information (topics on which we have dedicated articles in recent issues of our journal).15 For a general analysis of existence and comparative statics of equilibria in games with incomplete information see Athey (2001).16 The role of asymmetric information in competitive markets is at the core of a wide literature started with the analysis of adverse selection (Akerlof, 1970), signaling (Spence, 1973, Riley, 1975, 1979),17 screening (Rothschild and Stiglitz, 1976) and moral hazard (Pauly, 1974). When sellers have private information on the quality of the goods they want to trade, low quality goods tend to drive high quality goods out of a competitive market, unless: high quality sellers can signal their quality at a cost that is too high for the low quality sellers (for instance, providing a warranty), buyers can screen quality (requesting a rebate in case of low quality for a high price good), or sellers of low quality goods at high prices bear subsequent For more game-theoretic essays on trade see the Issue on Trade Policy of Research in Economics in June 2015. An extension of this model by Bertoletti (2016) was recently published in our journal. 15 On the related field of market design we should at least cite the seminal works on stable matching between two sets of players with given ordering of preferences (such as students and colleges) by Gale and Shapley (1962) and Roth (1984); for modern applications see Abdulkadiroglu and Sönmez (2003) and Che and Koh (2016). 16 A related work on the value of information in monotone decision problems by Athey and Levin (2017) will appear soon in these pages. 17 For classic discussions on refinements of signaling equilibria see Cho and Kreps (1987), Fudenberg and Tirole (1991) and Mailath, Okuno-Fujiwara and Postlewaite (1993), whose refinement is adopted by Palazzo in this volume. 13 14
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costs in the market (for instance, they cannot be active in the same market for a while). These insights have been at the basis of a large part of modern theories of market imperfections not only in goods’ markets but also in the labor and credit markets, and they have been investigated elsewhere also in our journal. Recent advances on market competition with adverse selection and moral hazard have been focused on the comparison with Walrasian outcomes,18 on extensions to imperfect competition between firms facing asymmetric information, and on dynamic contractual relations subject to asymmetric information.19 In dynamic competitive markets with asymmetric information, we can summarize some between the many insights emerging in the literature as follows: signaling may occur also by delaying trade of high quality expensive goods (a typical example is when high quality sellers are available to wait longer for a good deal),20 but pooling equilibria are also likely to emerge when incentive-compatible screening contracts are too costly (a typical example is bonusmalus insurance policies that gradually update risk premia for all buyers rather than inducing initial self-selection), and dynamic moral hazard aggravates problems of suboptimal production and risk allocation due to the distortions needed to incentivize effort (or, at the macroeconomic level, due to unemployment as a “discipline device” or credit rationing to reduce banks’ risk). Only recently the literature has started to consider search frictions in markets with informational asymmetries (Lauermann and Wolinski, 2016). Francesco Palazzo provides an interesting contribution to this literature in “Search costs and the severity of adverse selection”, which augments with search costs a dynamic model where sellers have private information on their products. He finds that, when search costs are relevant, high quality sellers signal their quality by delaying trade for a high price through a mechanism of intertemporal separation. However, when the search costs are low, only pooling equilibria emerge, with low quality sellers misrepresenting the quality of their products and demanding high prices: in such a case adverse selection is pervasive but an appropriate market design can mitigate its impact through an entry tax on sellers and a rebate after trade. In conclusion to our introduction to this Anniversary Issue, the vision of von Neumann and Morgenstern (1947) of reformulating economic theory on the basis of a general microfoundation of consumer behavior and equilibrium interactions between a small number of players has made big steps over the last 70 years.21 However, the most important achievement of game theory has been probably the creation of a coherent way of modeling and characterizing economic interactions, with applications that have by now reached any field of economics. We are pleased to add the following articles to this story while our journal reaches its 70th anniversary.
See Bennardo and Chiappori (2003) and Bisin and Gottardi (2006). Remarkable recent contributions to the dynamic principal-agent literature are in Levin (2003) and Sannikov (2008). 20 See Janssen and Roy (2002). 21 Von Neumann and Morgenstern (1947) already speculated on the opportunity of augmenting standard models of free competition and equilibrium market clearing with strategic interactions, when they noticed that “it is neither certain nor probable that a mere increase in the number of participants will always lead in fine to the conditions of free competition. The classical definitions of free competition all involve further postulates besides the greatness of that number” (pp. 14-15). For the introduction of strategic interactions in general equilibrium economics see the early work of Gabszewicz and Vial (1972) adopting Cournot competition between a fixed number of firms and the literature on imperfect competition between and endogenous number of firms in international trade and macroeconomics. 18 19
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Athey, Susan and Glenn Ellison, 2011, Position Auctions with Consumer Search, Quarterly Journal of Economics, 162, 3, 1213-70 Athey, Susan and Jonathan Levin, 2001, Information and competition in U.S. Forest Service Timber Auctions, Journal of Political Economy, 109, 2, 375-417 Athey, Susan and Jonathan Levin, 2017, The value of information in monotone decision problems, Research in Economics, forthcoming Battigalli, Pierpaolo, 2003, Rationalizability in infinite, dynamic games with incomplete information, Research in Economics, 57, 1, 1-38
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Bulow, Jeremy, Ming Huang and Paul Klemperer, 1999, Toeholds and takeovers, Journal of Political Economy, 107, 3, 427-54 Camerer, Colin, 2003, Behavioral Game Theory: Experiments in strategic interaction, Princeton University Press
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Chatterjee, Kalyan and William Samuelson, 1983, Bargaining under incomplete information, Operations Research, 31, 5, 835-51
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Che, Yeon-Koo and Youngwoo Koh, 2016, Decentralized College Admissions, Journal of Political Economy, 124, 5, 1295-338
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Cho, In-Koo and David Kreps, 1987, Signaling games and stable equilibria, Quarterly Journal of Economics, 102, 2, 179-222
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Choi, Chong Ju and Hyun Song Shin, 1992, A comment on a model of vertical product differentiation, Journal of Industrial Economics, 40, 2, 229-31
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Cooper, Russell, 1999, Coordination Games: complementarities and macroeconomics, Cambridge: Cambridge University Press Crawford, Vincent and Joel Sobel, 1982, Strategic information transmission, Econometrica, 50, 6, 1431-51 Crawford, Vincent, 1998, A survey of experiments on communication via cheap talk, Journal of Economic Theory, 78, 2, 286-98 Crawford, Vincent, 2003, Lying for strategic advantage: Rational and boundedly rational misrepresentation of intentions, American Economic Review, 93, 1, 133-149
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Ellison, Glenn and Drew Fudenberg, 2000, Learning purified mixed equilibria, Journal of Economic Theory, 90, 1, 84-115 Farrell, Joseph, 1987, Cheap talk, coordination, and entry, RAND Journal of Economics, 18, 1, 34-9 Fehr, Ernst, and Klaus M. Schmidt, 1999, A theory of fairness, competition, and cooperation, Quarterly Journal of Economics, 114, 3, 817-68
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Fudenberg, Drew, David M. Kreps, and Eric S. Maskin, 1990, Repeated games with long-run and short-run players, Review of Economic Studies, 57, 4, 555-73
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Fudenberg, Drew and David K. Levine, 1993, Self-confirming equilibrium, Econometrica, 61, 3, 523-545
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Fudenberg, Drew and David K. Levine, 1998, The Theory of Learning in Games, Cambridge: MIT Press
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Fudenberg, Drew and Eric Maskin, 1986, The Folk Theorem in Repeated Games with Discounting or with Incomplete Information, Econometrica, 54, 3, 533-54
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Fudenberg, Drew and Jean Tirole, 1991, Game Theory, Cambridge: MIT Press Gabszewicz, Jean and Jean-Philippe Vial, 1972, Oligopoly “a la Cournot” in a general equilibrium analysis, Journal of Economic Theory, 4, 381-400 Gabszewicz, Jean and Jacques Thisse, 1979, Price competition, qualities and income disparities, Journal of Economic Theory, 20, 3, 340-59 Gale, David and Lloyd S. Shapley, 1962, College admissions and the stability of marriage, The American Mathematical Monthly, 69, 1, 9-15 Gibbard, Allan, 1973, Manipulation of voting schemes: a general result, Econometrica, 41, 4, 587-601 10
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Green, Edward and Robert Porter, 1984, Noncooperative collusion under imperfect price information, Econometrica, 52, 1, 87-100 Greif, Avner, Paul Milgrom and Barry R. Weingast, 1994, Coordination, commitment, and enforcement: The case of the merchant guild, Journal of Political Economy, 102, 4, 745-776 Haltiwanger, John and Joseph Harrington, 1991, The impact of cyclical demand movements on collusive behavior, Rand Journal of Economics, 22, 1, 89-106
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Hansen, Robert, 1988, Auctions with endogenous quantity, RAND Journal of Economics, 19, 1, 44-58 Harsanyi, John, 1967-8, Games with Incomplete Information Played by Bayesian Players, Management Science, 14, 159-82, 320-34, 486-502
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Henrich, Joseph, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, Herbert Gintis, Richard McElreath, 2001, In search of homo economicus: behavioral experiments in 15 smallscale societies, American Economic Review, 91, 2, 73-78 Hillman, Arye and John Riley, 1989, Politically contestable rents and transfers, Economics & Politics, 1, 1, 17-39
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Hurwicz, Leonid, 1973, The design of mechanisms for resource allocation, American Economic Review, 63, 2, 1-30 Isaacs, Rufus, 1954, Differential games, Research Memorandum, U.S. Air Force Project RAND
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Itaya, Jun-ichi and Heinrich W. Ursprung, 2016, Price and death: modeling the death effect in art price formation, Research in Economics, 70, 3, 431-45
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Kandori, Michihiro, 1992, Social norms and community enforcement, Review of Economic Studies, 59, 1, 63-80
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Kandori, Michihiro, George J. Mailath and Rafael Rob, 1993, Learning, mutation, and long run equilibria in games, Econometrica, 61, 1, 29-56
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Klein, Benjamin and Keith Leffler, 1981, The role of market forces in assuring contractual performance, Journal of Political Economy, 89, 4, 615-41 Kováč, Eugen and Krešimir Žigić, 2016, Persistence of monopoly, innovation, and R&D spillovers, Research in Economics, 70, 4, 714-734 Kreps, David, Paul Milgrom, John Roberts, and Robert Wilson, 1982, Rational cooperation in the finitely repeated prisoners' dilemma, Journal of Economic Theory, 27, 2, 245-52 Kreps, David and Robert Wilson, 1982a, Sequential Equilibria, Econometrica, 50, 4, 863-94 Kreps, David and Robert Wilson, 1982b, Reputation and imperfect information, Journal of Economic Theory, 27, 253-79 11
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Lauerman, Stephan and Asher Wolinsky, 2016, Search with adverse selection, Econometrica, 84, 1, 243-315 Ledyard, John and Thomas Palfrey, 1999, A characterization of interim efficiency with public goods, Econometrica, 67, 2, 435-48 Levin, Jonathan, 2003, Relational incentive contracts, American Economic Review, 93, 3, 83557
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Mailath, George J., Masahiro Okuno-Fujiwara and Andrew Postlewaite, 1993, Belief-based refinements in signaling games, Journal of Economic Theory, 60, 2, 241-76 Mailath, George J. and Andrew Postlewaite, 1990, Asymmetric information bargaining problems with many agents, Review of Economic Studies, 57, 3, 351-67
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Mailath, George J. and Larry Samuelson, 2001, Who wants a good reputation?, Review of Economic Studies, 68, 2, 415-41. Mailath, George J. and Larry Samuelson, 2006, Repeated Games and Reputations. Long-run relationships, Oxford: Oxford University Press Maskin, Eric and John Riley, 2000, Asymmetric auctions, Review of Economic Studies, 67, 3, 413-38
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Maskin, Eric and Jean Tirole, 1988, A theory of dynamic oligopoly, I: Overview and quantity competition with large fixed costs, Econometrica, 56, 3, 549-69
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Milgrom, Paul, Douglass C. North and Barry Weingast, 1990, The role of institutions in the revival of trade: The law merchant, private judges, and the champagne fairs, Economics & Politics, 2, 1, 1-23
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Milgrom, Paul R. and Robert J. Weber, 1982, A theory of auctions and competitive bidding, Econometrica, 50, 5, 1089-122 Morris, Stephen, 2014, Coordination, timing and common knowledge, Research in Economics, 68, 4, 306-314 Morris, Stephen and Hyun Song Shin, 1998, Unique equilibrium in a model of self-fulfilling currency attacks, American Economic Review, 88, 3, 587-97 Morris, Stephen and Hyun Song Shin, 2002, Social value of public information, American Economic Review, 92, 5, 1521-34 Myerson, Roger B. , 1981, Optimal auction design, Mathematics of Operations Research, 6, 1, 58-73
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Nash, John, 1953, Two-person cooperative games, Econometrica, 21, 1, 128-40
O’Malley, Michelle, 2013, Painting under Pressure. Fame, Reputation and Demand in Renaissance Florence, New Haven: Yale University Press
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Pauly, Mark V., 1974, Overinsurance and public provision of insurance: the roles of moral hazard and adverse selection, Quarterly Journal of Economics, 88, 1, 44-62 Peleg, Bezalel, 1978, Consistent Voting Systems, Econometrica, 46, 1, 153-61
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Satterthwaite, Mark Allen, 1975, Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions, Journal of Economic Theory, 10, 2, 187-217 Schelling, Thomas, 1980, The Strategy of Conflict, Cambridge: Harvard University Press Selten, Reinard, 1965, Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragentragheit, Zeitschrift fur die gesamte Staatswissenschaft, 12, 201-324
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Vickrey, William, 1961, Counterspeculation, auctions, and competitive sealed tenders, Journal of Finance, 16, 1, 8-37 Von Neumann, John and Oscar Morgenstern, 1947, Theory of Games and Economic Behavior, 2nd Edition, Princeton: Princeton University Press
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Weitzman, Martin, 2017, Voting on Prices vs. Voting on Quantities in a World Climate Assembly, Research in Economic, forthcoming
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Research in Economics and Game Theory. A 70th Anniversary Federico Etro PII: DOI: Reference:
S1090-9443(17)30037-6 10.1016/j.rie.2017.02.001 YREEC 708
To appear in:
Research in Economics
Please cite this article as: Federico Etro , Research in Economics and Game Theory. A 70th Anniversary, Research in Economics (2017), doi: 10.1016/j.rie.2017.02.001
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Research in Economics and Game Theory. A 70th Anniversary
Federico Etro
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Editor in Chief of Research in Economics Department of Economics, Ca’ Foscari University, Italy
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This Special Issue of Research in Economics dedicated to Game Theory coincides with the 70th anniversary of the first issue of our journal, born indeed in 1947. We are delighted to celebrate this anniversary announcing that we have reached 300 submissions over the last year and announcing an important renovation of our Editorial Board. We welcome as new Coeditor Steve Levitt from the Department of Economics of the University of Chicago, one of the most brilliant empirical economists of the last decades and a recipient of the John Bates Clark Medal in 2003: his wide knowledge on applied economics represents a fundamental contribution for our journal. We are also pleased to welcome, as Co-editor, Paolo Bertoletti from the University of Pavia, an experienced microeconomist whose critical acumen represents a major addition to the editorial activity of the Board. Together with them a few exceptional economists have joined our Board as Associate Editors: Manuel Arellano (CEMFI, Spain), Claude d'Aspremont (Université Catholique de Louvain, Belgium), Robin Boadway (Queen׳s University, Canada), George Borjas (Harvard University, USA), Hong Bin Cai (Peking University, China), Andrea Colciago (Dutch National Bank, Netherlands), Ravi Kanbur (Cornell University, USA), Silvia Marchesi (University of Milan, Bicocca, Italy), Toshihiro Matsumura (University of Tokyo, Japan), Pierre Perron (Boston University, USA), Hashem Pesaran (University of Southern California, USA), Pierre Pestieau (CREPP, Université de Liège, Belgium), Assaf Razin (Tel-Aviv University, Israel), Harvey Rosen (Princeton University, USA) and Kenneth West (University of WisconsinMadison, USA). We are grateful to all of them for accepting these positions and to the past Coeditor Alberto Bisin and the past members of the Editorial Board who have completed their service with this issue. ***
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The following pages will introduce this Anniversary issue on game theory relating its articles to the general development of this field of applied math. As well known, game theory studies strategic interactions between decision-makers who maximize their expected payoffs. It was moving its first steps 70 years ago, just like our journal. Indeed, expected utility theory was founded on basic axioms of rational preferences in the Appendix to the 1947 Edition of the monumental book of John von Neumann and Oscar Morgenstern, “Theory of Games and Economic Behavior”, and provided the definitive microfoundation of standard economic models of rational behavior under uncertainty. Most of all, that book introduced the first comprehensive treatment of basic game theory, with a special focus on zero-sum games, which are basic games where the net gains of the players are null (as in Stone, Paper, Scissors), but also with the more ambitious aim of building a new approach to economic theory based on equilibrium interactions between a small number of rational players.
Email: [email protected].
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The next crucial step in the development of a formal theory of games was the definition and the characterization of an equilibrium concept. Nash (1950a, 1951) defined the notion of a non-cooperative equilibrium where the strategy of each player is the best response to the strategies of the other players, and proved existence of this equilibrium in mixed strategies (as in Stone, Paper, Scissors, where each player should randomize between the three options with equal probabilities): this is what we now call a Nash Equilibrium, which is regularly applied to static games where players act simultaneously (such as competition in quantities or in prices). Nash (1950b, 1953) introduced also a cooperative equilibrium concept for bargaining games and derived its axiomatic foundation.1 Selten (1965) refined the Nash equilibrium to the notion of SubGame Perfect Equilibrium, which is based on the fundamental principle of backward induction (in practice: first, understand what will happen tomorrow as a consequence of today’s choices, and, then, you can figure out what is your best choice for today) and is now the standard equilibrium concept for games with perfect information and multiple stages (such as leader-followers’ games or spatial games of location and pricing).2 Harsanyi (1967) introduced the Bayesian Equilibrium for games with incomplete information, where players maximize their expected utility under incomplete information and given the beliefs about each player’ type: later the concept was refined allowing agents to update their beliefs over time according to the Bayes’ rule on the equilibrium path and, in the Sequential Equilibrium developed by Kreps and Wilson (1982a), also off the equilibrium path.3 The last decades have seen an explosion of applications of game theory and new equilibrium concepts in virtually any field of economics as well as other social and natural sciences.4 Excellent textbook treatments can be found in Fudenberg and Tirole (1991), Myerson (1997) and Rasmusen (2006). The prisoner’s dilemma is probably the most famous non-cooperative game: each of two prisoners can either confess that the other committed a crime or cooperate by remaining silent, and they will serve 2 years each in prison if they both confess, 1 year if they are both silent and respectively 3 and 0 years if a prisoner is silent and the other does confess. The game, whose unique Nash equilibrium is (confess, confess), exemplifies why strategic interactions may generate inefficient results and makes us wonder whether and how players can reach better outcomes. This issue is fundamental to understand not only rational behavior of agents in the economy, but also the development of institutions and social behavior sustaining cooperation. Deep down, any interaction can be seen as a game, indeed as part of the “game of life”, and the outcome of any game depends at the end on its future consequences. In a series of celebrated contributions, the political scientist Axelrod (1980, 1981, 1984) has analyzed experimental foundations for cooperation based on a so-called “TIT-FOR-TAT” strategy in a finitely repeated prisoner’s dilemma. Such a strategy, which requires one to cooperate on the first move and then to reciprocate by doing whatever the other player did on the previous move, won the tournament organized by Axelrod between a variety of different strategies, suggesting that reciprocity is not only a social norm, but also a successful rule for selfish agents. Kreps et al. (1982) complemented these findings with a theoretical foundation for reciprocity based on the same TIT-FOR-TAT strategy, and started a fruitful literature of interdisciplinary investigations on the role of information in social interactions. After 35 years, Robert Axelrod opens our Anniversary Issue with a new Another important solution concept in cooperative game theory with a variety of applications is in Shapley (1953). 2 The classic work on bargaining games in a dynamic framework is by Rubinstein (1982). 3 Important works on bargaining games under incomplete information are by Chatterjee and Samuelson (1983), Myerson and Satterthwaite (1983) and Mailath and Postlewaite (1990). 4 Other equilibrium concepts include the Correlated Equilibrium (Aumann, 1974), the Coalition-Proof Equilibrium (Bernheim, Peleg and Whinston, 1987) and Renegotiation-Proof Equilibrium, the Markov Perfect Equilibrium (Maskin and Tirole, 1988) and the Self-Confirming Equilibrium (Fudenberg and Levine, 1993). 1
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interdisciplinary essay written with Larissa Forster on “How historical analogies in newspapers of five countries make sense of major events: 9/11, Mumbai and Tahrir Square”. This is the first quantitative analysis comparing historical analogies invoked in three major events of this century within newspapers from five countries, and it will be certainly a valuable contribution to our understanding of salience, framing of information and rhetoric in decision making. The battle of sexes is another famous game where members of a couple chose separately whether to go to the opera or to a sport match, with symmetric positive payoffs if they chose the same event and zero payoffs otherwise: this is a game in which multiple equilibria emerge. Entry games are another example: when entry of a certain number of identical firms in a market is endogenous, different combinations of entrants could emerge in a simultaneous entry game, even if their identity is inconsequential for the nature of the endogenous market structure. However multiple equilibria can be genuinely different in other contexts. Consider publications in an academic journal: this is considered a good journal if top researchers chose to submit relevant articles to it, but top researchers chose to submit there if the journal is considered a good one, which allows for both bad and good submission equilibria in the absence of some coordinating device. The analysis of coordination through cheap talk in pre-play communication was introduced in a pioneering work of Crawford and Sobel (1982),5 and is crucial for understanding which equilibria should emerge and how preplay communication and its metastructure (based on thinking, a common language, rethoric, unwritten rules, written laws and even the informal “authority” of some players) can induce coordinated beliefs in specific games or in the same “game of life”. Such a foundational analysis underlies the essays of Vincent Crawford (“Let’s talk it over: coordination via preplay communication with level-k thinking”) and of George Mailath, Stephen Morris and Andrew Postlewaite (“Laws and authority”). Crawford adopts a structural non-equilibrium model based on strategic thinking to analyze coordination in a battle of sexes, showing that communication helps coordination and, with moderate differences in preferences, the level-k coordination rate6 is likely to be higher than the mixed strategy equilibrium rate even without communication. Mailath, Morris and Postlewaite move to the analysis of social conventions and institutions and acknowledge that endorsing executive decisions, passing legislation or announcing court opinions are just symbolic actions that make no real change in the “game of life” unless they help to coordinate the beliefs of citizens on the effects of the law and therefore their behavior. Since only a theory of cheap talk in coordination games can be relevant to understand laws and authority, these authors develop a related theory on how and when individuals have, gain and lose authority. Game theory has been widely employed to analyze politics and social choice, from the first application of the Hotelling model to two-party electoral competition to the application of mechanism design in the vain attempt of constructing ideal social choice functions (Gibbard, 1973; Satterthwaite, 1975; Peleg, 1978). Bezalel Peleg and Hans Peters build on this last tradition their discussion on “Feasible elimination procedures in social choice: an axiomatic characterization”, which founds social choice functions resulting from a feasible elimination procedure (which in practice requires voters to report complete preferences over alternatives) on the axioms of anonymity, Maskin’s monotonicity and independent blocking. The authors argue also that this axiomatic characterization can be seen as an extension of the majority rule for two alternatives (May, 1952) to a choice rule for at least three alternatives in On preplay communication see also Farrell (1987) and Crawford (1998, 2003). On the aggregate implications of coordination games see Cooper (1999), the important applications of Diamond and Dybvig (1983) and Morris and Shin (1998, 2002) and the recent work of Morris (2014). 6 The definition of level-k thinking is recursive: A level-k player adopts the best response to level k-1 players, with level-0 players acting randomly. 5
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a direct democracy. The essay on “Strategic dissent in the Hotelling-Downs model with sequential entry and private information” by Siddhartha Bandyopadhyay, Manaswini Bhalla, Kalyan Chatterjee and Jaideep Roy extends the classic model of electoral competition in a representative democracy to sequential entry of multiple office-seeking candidates with privately known qualities: the authors show that high-quality politicians signal their type adopting extreme ideological platforms compared to the median voter (while low-quality politicians randomize between mis-signaling quality and staying out of competition), which provides a new rationale for political polarization. Finally, the interaction of executive, legislative and judicial branches is the focus of the analysis of Jonathan Hamilton and Steven Slutsky (“Judicial review and the power of the executive and legislative branches”), which builds on their earlier design of efficient redistributive schemes in the presence of asymmetric information (Brito, Hamilton, Slutsky and Stiglitz, 1990).7 Both these two essays adopt the sequential equilibrium as their equilibrium concept. The development of behavioral game theory is one of the most interesting recent developments in theoretical and experimental research.8 For instance, it is well known that the strict logic of equilibrium and backward induction is often in contradiction with the way agents manage to commit to strategies in real life and in experimental situations.9 This emerges not only in finitely repeated prisoner’s dilemma games, but also in other dynamic games such as in the “Chain Store” game of Selten (1978) about entry deterrence of a sequence of competitors and in a variety of public goods’ games, where agents tend to contribute much more in experiments compared to the level of free-riding implied by a Nash equilibrium (see, for instance, Henrich et al., 2001). Imperfect information on the type of other players can help solving some of these paradoxes, as shown by Kreps et al. (1982) for the repeated prisoner’s dilemma and by Kreps and Wilson (1982b) for the chain store paradox. However, it is insufficient to explain what appears as a genuinely social behavior in other games, such as public good’s games or the “ultimatum game”, where an agent proposes how to split a prize and then a responder can either accept this or throw away the prize. Following the recent literature on behavioral game theory, Friedel Bolle has addressed this difficulty adopting social preferences based on inequality aversion (Fehr and Schmidt, 1999) or altruism and fairness (Rabin, 1993). His experiment tests these preferences in the “Passing the Buck” game, a new interesting dynamic game where multiple members of a group decide sequentially whether or not to incur costs so that they can fix a certain problem for the benefit of the group. The predicted unique Perfect Bayesian Equilibrium with incomplete information on the social preferences of the other players generally fits the experimental results. The analysis of strategic commitments in market competition is a traditional field of application of game theory to economics. Classic results have been derived within three classes of models that are now at the basis of the theory of duopoly. These were developed in the works of Dixit (1979) on quantity commitments by a Stackelberg leader, d’Aspremont, Gabszewicz and Thisse (1979) on location strategies with subsequent price competition between two firms, and Gabszewicz and Thisse (1979) on price competition between two firms producing vertically differentiated products.10 In this issue we present three essays that generalize these fundamental two-stage games.11 The Stackelberg game of quantity For further analysis of game-theoretic models of political science see the Special Issue on Political Economy of Research in Economics in September 2015 and, for an application to the political economy of international unions coordinating environmental policy, see Weitzman (2017). 8 For a comprehensive account of the literature we refer to Camerer (2003) and to Crawford, Costa-Gomes and Iriberri (2013) on strategic thinking, which is also the subject of the essay of Crawford in this volume. 9 For classic interdisciplinary applications see Schelling (1980). 10 Qualities of the two products were endogenized only later (see Choi and Shin, 1992). 11 For further analysis of game-theoretic models of strategic interactions see the Special Issue on Industrial Organization of Research in Economics in December 2016. 7
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competition with exogenous and endogenous entry is generalized by Antonio Tesoriere in “Stackelberg equilibrium with many leaders and followers. The case of zero fixed costs”: using lattice theoretical methods, the author provides a set of conditions for the existence of an equilibrium in pure strategies and characterizes nature and comparative statics of the equilibrium market structure when there are no entry costs. The Hotelling game is generalized by Jeroen Hinloopen and Stephen Martin in “Costly location in Hotelling duopoly”, which derives a set of conditions for the existence of an equilibrium in pure strategies and characterizes nature and comparative statics of the equilibrium locations. Finally, the Gabszewicz-Thisse model is generalized by Jean Gabszewicz, Marco Marini and Ornella Tarola in “Vertical differentiation and collusion: pruning or proliferation?”, where the authors characterize equilibrium qualities and prices in the presence of multiproduct firms. A supergame is an infinitely repeated game where cooperation can be sustainable as a SubGame Perfect Equilibrium as long as the players are patient enough, even if cooperation is not an equilibrium of the one-shot game. For instance, in the Prisoner’s Dilemma this happens with a so-called “grim trigger” strategy, which requires one to cooperate on the first move and then as long as cooperation takes place, but revert to the static Nash equilibrium strategy forever after a defection. More general treatments of such a Folk Theorem (a label due to the fact that the basic idea circulated between game theorists before being published) can be found in the works of Fudenberg and Maskin (1986) and Abreu (1988) which exploit the recursive nature of these games adopting punishments for deviators that minmax their payoffs, with a sort of “stick and carrot” structure. The literature has then derived a variety of Folk Theorems for supergames with short-lived players (Fudenberg, Kreps and Maskin, 1990), imperfect monitoring of actions (Abreu, Pearce and Stacchetti, 1990), random matching of players (Kandori, 1992, Ellison, 1994), private monitoring and any possible combination of these complications, culminating in the nice book of Mailath and Samuelson (2006).12 For interesting applications of models with random matching we recommend the works of Milgrom, North and Weingast (1990) and Greif, Milgrom and Weingast (1994) on cooperation in Medieval trade relationships. However, the main economic application of the theory of supergames is in the analysis of price-fixing cartels, where firms share a tacit understanding to raise prices. This form of collusion has been studied under noisy prices (Green and Porter, 1984), demand uncertainty (Haltiwanger and Harrington, 1991), private information on costs (Athey and Bagwell, 2001) and other extensions, characterizing when collusion is sustainable and at which prices. Instead, little is known about the type and strength of the mutual beliefs that can result in coordination and about the dynamic process that can lead from competitive to supracompetitive prices. On this topic we present an important work by Joseph Harrington Jr., “A Theory of collusion with partial mutual understanding”. Building on the concept of rationalizability in supergames with incomplete information, introduced in our journal by Battigalli (2003), the author provides a new foundation for paths toward tacit collusion based on mutual beliefs. Firms are assumed to commonly believe that price increases will be at least matched by the other firms, but lack any shared understanding about which firm will be the price leader, when this will increase its price and at which level: nevertheless, Harrington derives sufficient conditions for the emergence of supracompetitive prices and shows that these are bounded below the maximal equilibrium price. On the related literature on learning in games and evolutionary games see, inter alia, Kandori, Mailath and Rob (1993), Ellison (2000), Ellison and Fudenberg (2000) and the book of Fudenberg and Levine (1998). For an application of evolutionary theory to a compliance game see Petrohilos-Andrianos and Xepapadeas (2017). A somewhat related line of research in dynamic game theory, started by Isaacs (1954), concerns differential games in continuous time (for applications recently published in our journal see Itaya and Ursprung, 2016 and Kováč and Žigić, 2016). 12
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Building a reputation in repeated games has been the focus of a variety of theoretical investigations, from the model of Klein and Leffler (1981), where the expectation of repeat purchases of high quality experience goods at a price premium provides the incentives to deliver high quality, to models à la Kreps et al. (1982) where reputation to act in a virtuous way is built through persistent imitation of a committed type of player, to the more recent model of Mailath and Samuelson (2001) where reputation is built by exerting effort to benefit from separation in the market from an uncommitted type of player (for an interesting application to reputation building of artists in Renaissance Florence see O’Malley, 2013). An interesting review of the different theoretical approaches trying to capture the idea of reputation can be found in the book of Mailath and Samuelson (2006). In our volume, Eric Rasmusen builds on the Klein-Leffler approach to develop “A model of trust in quality and North-South trade”. This essay explains trade between identical countries in a general equilibrium framework where a country exports experience goods of high quality and high price whose reputation is sustainable in the long run, and imports cheaper low quality goods from another country. In line with modern trade theories, the analysis accounts for equilibrium in each national labor market and endogenous entry of high quality firms through investments in a non-price dimension.13 The analysis of mechanism design through the principle of incentive compatibility (Hurwicz, 1973) has been a fertile territory to exploit game theoretic analysis. The first application to a market setting has been to auctions (Vickrey, 1961), whose design has been studied in a variety of contexts, from complete information (Hillman and Riley, 1989)14 to incomplete information (Myerson, 1981, Riley and Samuelson, 1981, Milgrom and Weber, 1982), and in extensions with endogenous quantities (Hansen, 1988), common values (Bulow, Huang and Klemperer, 1999), asymmetries (Maskin and Riley, 2000) and multidimensionality (Athey and Levin, 2001; Athey and Ellison, 2011). The same principles of mechanism design under incomplete information have been applied to many other fields, including social choice and provision of public goods (d'Aspremont and Gérard-Varet, 1979; Ledyard and Palfrey, 1999), war of attritions (Bulow and Klemperer, 1999), optimal non-linear taxation and principal-agent contracts where the productivity of agents exerting effort is private information (topics on which we have dedicated articles in recent issues of our journal).15 For a general analysis of existence and comparative statics of equilibria in games with incomplete information see Athey (2001).16 The role of asymmetric information in competitive markets is at the core of a wide literature started with the analysis of adverse selection (Akerlof, 1970), signaling (Spence, 1973, Riley, 1975, 1979),17 screening (Rothschild and Stiglitz, 1976) and moral hazard (Pauly, 1974). When sellers have private information on the quality of the goods they want to trade, low quality goods tend to drive high quality goods out of a competitive market, unless: high quality sellers can signal their quality at a cost that is too high for the low quality sellers (for instance, providing a warranty), buyers can screen quality (requesting a rebate in case of low quality for a high price good), or sellers of low quality goods at high prices bear subsequent For more game-theoretic essays on trade see the Issue on Trade Policy of Research in Economics in June 2015. An extension of this model by Bertoletti (2016) was recently published in our journal. 15 On the related field of market design we should at least cite the seminal works on stable matching between two sets of players with given ordering of preferences (such as students and colleges) by Gale and Shapley (1962) and Roth (1984); for modern applications see Abdulkadiroglu and Sönmez (2003) and Che and Koh (2016). 16 A related work on the value of information in monotone decision problems by Athey and Levin (2017) will appear soon in these pages. 17 For classic discussions on refinements of signaling equilibria see Cho and Kreps (1987), Fudenberg and Tirole (1991) and Mailath, Okuno-Fujiwara and Postlewaite (1993), whose refinement is adopted by Palazzo in this volume. 13 14
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costs in the market (for instance, they cannot be active in the same market for a while). These insights have been at the basis of a large part of modern theories of market imperfections not only in goods’ markets but also in the labor and credit markets, and they have been investigated elsewhere also in our journal. Recent advances on market competition with adverse selection and moral hazard have been focused on the comparison with Walrasian outcomes,18 on extensions to imperfect competition between firms facing asymmetric information, and on dynamic contractual relations subject to asymmetric information.19 In dynamic competitive markets with asymmetric information, we can summarize some between the many insights emerging in the literature as follows: signaling may occur also by delaying trade of high quality expensive goods (a typical example is when high quality sellers are available to wait longer for a good deal),20 but pooling equilibria are also likely to emerge when incentive-compatible screening contracts are too costly (a typical example is bonusmalus insurance policies that gradually update risk premia for all buyers rather than inducing initial self-selection), and dynamic moral hazard aggravates problems of suboptimal production and risk allocation due to the distortions needed to incentivize effort (or, at the macroeconomic level, due to unemployment as a “discipline device” or credit rationing to reduce banks’ risk). Only recently the literature has started to consider search frictions in markets with informational asymmetries (Lauermann and Wolinski, 2016). Francesco Palazzo provides an interesting contribution to this literature in “Search costs and the severity of adverse selection”, which augments with search costs a dynamic model where sellers have private information on their products. He finds that, when search costs are relevant, high quality sellers signal their quality by delaying trade for a high price through a mechanism of intertemporal separation. However, when the search costs are low, only pooling equilibria emerge, with low quality sellers misrepresenting the quality of their products and demanding high prices: in such a case adverse selection is pervasive but an appropriate market design can mitigate its impact through an entry tax on sellers and a rebate after trade. In conclusion to our introduction to this Anniversary Issue, the vision of von Neumann and Morgenstern (1947) of reformulating economic theory on the basis of a general microfoundation of consumer behavior and equilibrium interactions between a small number of players has made big steps over the last 70 years.21 However, the most important achievement of game theory has been probably the creation of a coherent way of modeling and characterizing economic interactions, with applications that have by now reached any field of economics. We are pleased to add the following articles to this story while our journal reaches its 70th anniversary.
See Bennardo and Chiappori (2003) and Bisin and Gottardi (2006). Remarkable recent contributions to the dynamic principal-agent literature are in Levin (2003) and Sannikov (2008). 20 See Janssen and Roy (2002). 21 Von Neumann and Morgenstern (1947) already speculated on the opportunity of augmenting standard models of free competition and equilibrium market clearing with strategic interactions, when they noticed that “it is neither certain nor probable that a mere increase in the number of participants will always lead in fine to the conditions of free competition. The classical definitions of free competition all involve further postulates besides the greatness of that number” (pp. 14-15). For the introduction of strategic interactions in general equilibrium economics see the early work of Gabszewicz and Vial (1972) adopting Cournot competition between a fixed number of firms and the literature on imperfect competition between and endogenous number of firms in international trade and macroeconomics. 18 19
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