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on Game Theory |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, Princeton University) |
| Abstract: | We describe a methodology for making counterfactual predictions when the information held by strategic agents is a latent parameter. The analyst observes behavior which is rationalized by a Bayesian model in which agents maximize expected utility, given partial and differential information about payoff-relevant states of the world. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of and agents’ information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, there is a finite dimensional description of the sharp counterfactual prediction, even though the latent parameter, the type space, is infinite dimensional. |
| Keywords: | Counterfactuals, Bayes correlated equilibrium, Information structure, Type space, Linear program |
| JEL: | C72 D44 D82 D83 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2162r&r=all |
| By: | Ashish Agarwal; Kedar Dhamdhere; Mukund Sundararajan |
| Abstract: | We study interactions among players in cooperative games. We propose a new interaction index called Shapley-Taylor interaction index. It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the Taylor series represents a function in terms of its derivatives of various orders. We axiomatize the method using the standard Shapley axioms--linearity, dummy, symmetry and efficiency--and also an additional axiom that we call the interaction distribution axiom. This new axiom explicitly characterizes how inter-actions are distributed for a class of games called interaction games. We contrast the Shapley-Taylor interaction index against the previously pro-posed Shapley Interaction index and the Banzhaf interaction index (cf. [2]). |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1902.05622&r=all |
| By: | Philip J. Grossman (Monash University); Youngseok Park (Colby College); Jean Paul Rabanal (Monash University); Olga A. Rud (RMIT Univeristy) |
| Abstract: | We conduct a laboratory experiment to study the role of gender on social welfare outcomes in a strategic commitment game of incomplete information. In our baseline treatment, players simultaneously commit to either a Hawkish action, which leads to a private payoff, or a Dovish action, which can enhance social welfare. We add a sequential and an endogenous move treatment, where in the former, the first mover is exogenously selected and in the latter, players self-select the order of play. The two additional treatments relax the commitment constraint for the second mover. We find that (i) social welfare is significantly improved in the last two treatments and (ii) the outcome in the endogenous move treatment is mainly driven by gender. Men are willing to play the risky Dovish action more often than women. |
| Keywords: | Gender, type uncertainty, endogenous timing, laboratory experiment |
| JEL: | C72 C92 D82 D91 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:apc:wpaper:141&r=all |
| By: | Hagenbach, Jeanne; Koessler, Frédéric |
| Abstract: | This paper proposes an equilibrium concept, Language-Based Expectation Equilibrium, which accounts for partial language understanding in sender-receiver cheap talk games. Each player has a privately known language competence representing all the messages that he understands. For the messages he does not understand, he has correct but coarse expectations about the equilibrium strategies of the other player. In general, a language-based expectation equilibrium outcome differs from Nash and communication equilibrium outcomes, but is always a Bayesian solution. Partial language competence of the sender rationalizes information transmission and lies in pure persuasion problems, and facilitates information transmission from a moderately biased sender. |
| Keywords: | analogy-based expectations; Bayesian solution; bounded rationality; cheap talk; Language |
| JEL: | C72 D82 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13488&r=all |
| By: | Hideo Konishi (Boston College); Chen-Yu Pan (Wuhan University) |
| Abstract: | We consider a sequential formation of alliances à la Bloch (1996) and Okada (1996) followed by a two-stage contest in which alliances first compete with each other, and then the members in the winning alliance compete again for an indivisible prize. In contrast to Konishi and Pan (2019) which adopted an open-membership game as the alliance formation process, alliances are allowed to limit their memberships (excludable alliances). We show that if members' efforts are strongly complementary to each other, there will be exactly two asymmetric alliances the larger alliance is formed first and then the rest of the players form the smaller one. This result contrasts with the one under open membership, where moderate complementarity is necessary to support a two-alliance structure. It is also in stark contrast with Bloch et al. (2006), where they show that a grand coalition is formed in the same game if the prize is divisible and a binding contract is possible to avoid further conflicts after an alliance wins the prize. |
| Keywords: | contest, alliance, coalition formation, complementarity |
| JEL: | D23 D72 D74 |
| Date: | 2019–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:973&r=all |
| By: | Besner, Manfred |
| Abstract: | A new concept for TU-values, called value dividends, is introduced. Similar to Harsanyi dividends, value dividends are defined recursively and provide new characterizations of values from the Harsanyi set. In addition, we generalize the Harsanyi set where each of the TU-values from this set is defined by the distribution of the Harsanyi dividends via sharing function systems and give an axiomatic characterization. As a TU value from the generalized Harsanyi set, we present the proportional Harsanyi payoff, a new proportional solution concept. As a side benefit, a new characterization of the Shapley value is proposed. None of our characterizations uses additivity. |
| Keywords: | TU-game · Value dividends · (Generalized) Harsanyi set · Weighted Shapley values · (Proportional) Harsanyi payoff · Sharing function systems |
| JEL: | C7 C71 |
| Date: | 2019–02–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92247&r=all |
| By: | Bosetti, Valentina; Heugues, Melanie; Tavoni, Alessandro |
| Abstract: | We explore the prospects of cooperation in a threshold public bad game. The experiment’s setup allows us to investigate the issue of effort coordination between signatories and non-signatories to a climate agreement under the threat of a catastrophe. Motivated actors may signal willingness to lead by committing a share of investments to a ‘clean’ but less remunerative project. The game is parametrized such that the externality cannot be fully internalized by the coalition, so that some effort on the part of the second movers is required if the catastrophic losses are to be avoided. We manipulate both the relative returns of two investments and the extent to which the gains from leadership diffuse to second movers. We find that the likelihood of reaching a sizeable coalition of early investors in the clean technology is higher when the benefits are appropriated by the coalition. Conversely, spillovers can entice second movers’ adoption. |
| JEL: | C70 C92 Q50 |
| Date: | 2017–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:68931&r=all |
| By: | Santiago J. Rubio (Department of Economic Analysis and ERI-CES, University of Valencia) |
| Abstract: | This paper studies the impact of adaptation on the stability of an international emission agreement. To address this issue we solve a three-stage coalition formation game where in the first stage countries decide whether or not to sign the agreement. Then, in the second stage, signatories (playing together) and non-signatories (playing individually) select their levels of emissions. Finally, in the third stage, each country decides on its level of adaptation non co-operatively. We solve this game for two models. For both, it is assumed that damages are linear with respect to emissions which guarantee that emissions are strategic complements in the second stage of the game. However, for the first model adaptation reduces the marginal damages of emissions in a multiplicative way whereas for the second model the reduction occurs in an additive way. Our analysis shows that the models yield different predictions in terms of participation. In the first case, we find that the larger the gains of full cooperation, the larger the cooperation. However, in the second case, the unique stable agreement we find consists of three countries regardless of the gains of full cooperation. These results suggest that complementarity can play in favor of cooperation but that it is not a sufficient condition to obtain more participation in an emission agreement. Finally, we would like to point out that our research indicates that the way adaptation reduces damages plays a critical role over the outcome of the coalition formation game. |
| Keywords: | International Environmental Agreements, Mitigation-Adaptation Game, Strategic Complements |
| JEL: | D62 F53 H41 Q54 |
| Date: | 2018–08 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2018.29&r=all |
| By: | Suehyun Kwon |
| Abstract: | This paper points out issues with having behavioral players together with fully rational players in a game. One example of behavioral players is naive or sophisticated players; one can study higher-order beliefs when sophistication is the first-order belief, but the paper also considers alternative ways of modelling the type space and non-Bayesian updating. The paper shows that players must have heterogeneous priors and this type of heterogeneous priors cannot be justified by acquiring private information from the common prior. Furthermore, equilibrium definitions need to be modified for games with behavioral players. |
| Keywords: | naivete, misspecified beliefs, heterogeneous priors, higher-order beliefs, equilibrium definition, Harsanyi doctrine |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7504&r=all |
| By: | Hoppe-Wewetzer, Heidrun C.; Katsenos, Georgios; Ozdenoren, Emre |
| Abstract: | This paper offers a model of experimentation and learning with uncertain outcomes as suggested by Arrow (1969). Investigating a two-player stopping game, we show that competition leads to less experimentation, which extends existing results for preemption games to the context of experimentation with uncertain outcomes. Furthermore, we inquire about the extent of experimentation under two information settings: when the researchers share information about the outcomes of their experiments and when they do not share such information. We discover that the sharing of information can generate more experimentation and higher value for a relatively wide range of parameters. We trace this finding to the stronger ability to coordinate on the information obtained through experimentation when it is shared. Our model allows to shed light on recent criticism of the current scientific system. |
| JEL: | D83 O31 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13483&r=all |
| By: | Charles Bellemare; Alexander Sebald |
| Abstract: | We derive bounds on the causal effect of belief-dependent preferences (reciprocity and guilt aversion) on choices in sequential two-player games without exploiting information or data on the (higher-order) beliefs of players. We show how informative bounds can be derived by exploiting a specific invariance property common to those preferences. We illustrate our approach by analyzing data from an experiment conducted in Denmark. Our approach produces tight bounds on the causal effect of reciprocity in the games we consider. These bounds suggest there exists significant reciprocity in our population – a result also substantiated by the participants’ answers to a post-experimental questionnaire. On the other hand, our approach yields high implausible estimates of guilt aversion. We contrast our estimated bounds with point estimates obtained using data on self-declared higher-order beliefs, keeping all other aspects of the model unchanged. We find that point estimates fall within our estimated bounds suggesting that elicited higher-order belief data in our experiment is weakly (if at all) affected by a potential endogeneity problem due to e.g. false consensus effects. |
| Keywords: | belief-dependent preferences, partial identification |
| JEL: | C93 D63 D84 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7505&r=all |
| By: | Gérard Mondello (Groupe de Recherche en Droit, Economie et Gestion); Evens Salies (Observatoire français des conjonctures économiques) |
| Abstract: | Summary: This paper extends the basic unilateral accident model to allow for Cournot competition. Two firms compete with production input and prevention as strategic variables under asymmetric capacity constraints. We find that liability regimes exert a crucial influence on the equilibrium price and outputs. Strict liability leads to higher output and higher risk compared to negligence. We also study the conditions under which both regimes converge. Key Words: Tort Law, Strict |
| Keywords: | Tort Law; Strict liability; Negligence Rule; Imperfect competition; Oligopoly; Cournot competition |
| JEL: | D43 L13 L52 K13 |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/5a1unjmoh881mrfbrlqhebkbba&r=all |
| By: | Pradeep Dubey (SUNY); John Geanakoplos (Cowles Foundation, Yale University) |
| Abstract: | We consider the Rothschild-Stiglitz model of insurance but without the exclusivity constraint. It turns out that there always exists a unique equilibrium, in which the reliable and unreliable consumers take out a primary insurance up to its quantity limit, and the unreliable take out further secondary insurance at a higher premium. We provide a simple proof of this result (extended to multiple types of consumers) with the hope that it may be pedagogically useful. |
| Keywords: | Non-exclusive insurance, Free entry, Adverse selection, Primary-secondary insurance |
| JEL: | D43 D82 D86 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2167&r=all |
| By: | Korkut Alp Erturk |
| Abstract: | The paper explores how elites can develop capacity for collective agency through coordination. Elites’ challenge is to simultaneously deter the state from abusing power while at the same time relying on it to discipline defectors in their midst. The basic insight holds that the credibility of the state’s threats depends on the cost of carrying them out, which elites can have control over if they can act in tandem. Elites can coordinate in being compliant when the ruler’s threats serve their collective interest which raises the threats’ credibility, while lowering that of those they dislike by their coordinated noncompliance making them costly to carry out. |
| Keywords: | elite collective agency, state power, coordination, credible threats, subgame imperfect equilibrium |
| JEL: | C72 D72 D02 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:uta:papers:2019_04&r=all |
| By: | Helland, Eric; Sovinsky, Michelle |
| Abstract: | Every year thousands of firms are engaged in research joint ventures (RJV), where knowledge gained through R&D is shared among members. Many members are rivals leaving open the possibility that firms form RJVs to facilitate product collusion. We exploit variation in RJV formation generated by a policy change that affects the collusive benefits but not the research synergies of a RJV. Estimates from our RJV participation equation indicate participation is impacted by the policy change. The magnitude is significant with an average drop in the probability of joining of 30%. Our results are consistent with RJVs serving a collusive function. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13533&r=all |
| By: | Yu Zhu; Scott Hendry |
| Abstract: | This paper considers an economy where central-bank-issued fiat money competes with privately issued e-money. We study a policy-setting game between the central bank and the e-money issuer and find (1) the optimal monetary policy of the central bank depends on the policy of the private issuer and may deviate from the Friedman rule; (2) there may exist multiple equilibria; (3) when the economy approaches a cashless state, the central bank’s optimal policy improves the market power of the e-money issuer and can lead to a discrete decrease in welfare and a discrete increase in inflation; and (4) first best cannot be achieved. Central-bank-issued e-money leads to a simple optimal policy that achieves the first best. |
| Keywords: | Digital Currencies; Monetary Policy |
| JEL: | E52 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:19-1&r=all |
| By: | Henning Finseraas; Torbjørn Hanson; Åshild A. Johnsen; Andreas Kotsadam; Gaute Torsvik |
| Abstract: | We study how close personal contact with minorities affects in-group and out-group trust in a field experiment in the armed forces. Soldiers are randomly assigned to rooms with or without ethnic minorities. At the end of the recruit period, we measure trust by using a trust game. Results indicate that close personal contact with minorities increases trust towards a generic immigrant. We replicate the result that individuals coming from more ethnically diverse areas trust minorities less, but random assignment to interact with minority soldiers removes this negative correlation. We conclude that social integration involving personal contact can reduce negative effects of ethnic diversity on trust. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7515&r=all |
| By: | Nadja R. Ging-Jehli; Florian H. Schneider; Roberto A. Weber |
| Abstract: | We experimentally study settings where an individual may have an incentive to adopt negative beliefs about another’s intentions in order to justify egoistic behavior. Our first study uses a game in which a player can take money from an opponent in order to prevent the opponent from subsequently causing harm. We hypothesize that players will justify taking by engaging in “strategic cynicism,” convincing themselves of the opponent’s ill intentions. We elicit incentivized beliefs both from players with such an incentive and from neutral third parties with no incentive to bias their beliefs. We find no difference between the two sets of beliefs, suggesting that people do not negatively bias their beliefs about a strategic opponent even when they have an incentive to do so. This result contrasts with Di Tella, et al. (2015), who argue that they provide evidence of strategic cynicism. We reconcile the discrepancy by using Di Tella, et al.’s, data, a simple model of strategic belief manipulation and a novel experiment in which we replicate Di Tella, et al.’s, experiment and also elicit the beliefs of neutral third parties. Across three experimental datasets, the results provide no evidence of negatively biased beliefs about others’ intentions. However, Di Tella, et al.’s, results and our novel data indicate that those with a greater incentive to view others’ intentions negatively exhibit relatively less positive beliefs than those without such incentives. |
| Keywords: | motivated beliefs, strategic cynicism, bias, experiment |
| JEL: | C72 D83 C92 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7517&r=all |
| By: | Daniel Spiro |
| Abstract: | This paper explores intergenerational transmission of culture and the consequences of a plausible assumption: that people care not only for their children’s culture but also for how their grand-children are raised. This departs from the previous literature which, without exception, assumes parents either do not care about, or fail to consider, the effect their actions have on all future generations. The current paper models a sequential game where parents take actions trading off being close to their own preferences and influencing their children, and where parents take into account that the children face a similar trade-off when raising their children. Predictions regarding endogenous extremism, the effect of societal socialization, parents. discounting, social pressure and interaction between groups are derived. In equilibrium, parents behave more extremely than their own preferences and this effect is intensified the more extreme preferences the parent has. There may be perpetual extremizing whereby an arbitrarily long sequence of generations will behave more extremely than the first ancestor’s preferences. Furthermore, interaction of groups implies more extreme initial behavior but also faster integration. |
| Keywords: | culture, integration, social pressure |
| JEL: | D90 J15 Z10 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7507&r=all |
| By: | Giebe, Thomas; Lee, Miyu |
| Abstract: | There are legal grounds to hear competitors in merger control proceedings, and competitor involvement has gained significance. To what extent this is economically sensible is our question. The competition authority applies some welfare standard while the competitor cares about its own profit. In general, but not always, this implies a conflict of interest. We formally model this setting with cheap talk signaling games, where hearing the competitor might convey valuable information to the authority, but also serve the competitor's own interests. We find that the authority will mostly have to ignore the competitor but, depending on the authority's own prior information, strictly following the competitor's selfish recommendation will improve the authority's decision. Complementary to our analysis, we provide empirical data of competitor involvement in EU merger cases and give an overview of the legal discussion in the EU and US. |
| Keywords: | merger control, antitrust, European Commission, signaling, efficiency, competitors, rivals, competition |
| JEL: | C73 G34 K21 K4 L13 L2 L4 |
| Date: | 2019–02–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62428&r=all |