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on Game Theory |
| By: | Bergemann, Dirk; Morris, Stephen |
| Abstract: | Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persua- sion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. |
| Keywords: | Bayesian persuasion; correlated equilibrium; incomplete information; information design; information structure.; robust predictions |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11867&r=gth |
| By: | Koichi Futagami (Graduate School of Economics, Osaka University); Toshihiro Matsumura (Institute of Social Science, The University of Tokyo); Kizuku Takao (Department of Economics, Aomori Public University) |
| Abstract: | Previous studies in differential games reveal that intertemporal strategic behaviors have an important role for various economic problems. However, most of their analyses are limited to cases where objective functions are identical among agents. In this paper, we characterize the open-loop Nash equilibrium and the Markov perfect Nash equilibrium of a mixed duopoly game where a fully or partially state-owned firm and a fully private firm compete in the quantities of homogeneous goods with sticky prices. We show that in the Markov perfect Nash equilibrium, an increase in the governments f share-holdings of the state-owned firm has a non-monotonic effect on the price, and in a wide range of parameter spaces, it increases the price. These results are derived from the interaction of an asymmetric structure of agents f objectives and inter-temporal strategic behaviors, which are in sharp contrast with those in the open-loop Nash equilibrium. We provide new implications for privatizationpolicies in the presence of dynamic interactions, against the static analyses. |
| Keywords: | Mixed Duopoly, Open-loop Nash equilibrium, Markov Perfect Nash equilibrium |
| JEL: | C73 D43 L32 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:osk:wpaper:1703&r=gth |
| By: | Bernhard von Stengel |
| Abstract: | We consider a sequential inspection game where an inspector uses a limited number of inspections over a larger number of time periods to detect a violation (an illegal act) of an inspectee. Compared with earlier models, we allow varying rewards to the inspectee for successful violations. As one possible example, the most valuable reward may be the completion of a sequence of thefts of nuclear material needed to build a nuclear bomb. The inspectee can observe the inspector, but the inspector can only determine if a violation happens during a stage where he inspects, which terminates the game; otherwise the game continues. Under reasonable assumptions for the payoffs, the inspector’s strategy is independent of the number of successful violations. This allows to apply a recursive description of the game, even though this normally assumes fully informed players after each stage. The resulting recursive equation in three variables for the equilibrium payoff of the game, which generalizes several other known equations of this kind, is solved explicitly in terms of sums of binomial coefficients. We also extend this approach to nonzero-sum games and “inspector leadership” where the inspector commits to (the same) randomized inspection schedule, but the inspectee acts legally (rather than mixes as in the simultaneous game) as long as inspections remain. |
| Keywords: | inspection game; multistage game; recursive game; Stackelberg leadership; binominal coefficients |
| JEL: | C72 |
| Date: | 2016–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:68299&r=gth |
| By: | Paula Jaramillo; Ça?atay Kay?; Flip Klijn |
| Abstract: | This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight. |
| Keywords: | Matching, roommate problem, stability, core, rank gap, bound |
| JEL: | C78 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:956&r=gth |
| By: | Ramon Cobo-Reyes (Department of Economics, University of Exeter); Gabriel Katz (Department of Politics, University of Exeter); Simone Meraglia? (Department of Economics, University of Exeter) |
| Abstract: | We experimentally analyze the effect of the endogenous choice of sanctioning institutions on cooperation and migration patterns across societies. In our experiment, subjects are allocated to one of two groups, are endowed with group-specific preferences, and play a public goods game for 30 periods. Each period, subjects can move between groups and, at fixed intervals, can vote on whether to implement formal (centralized) sanctioning institutions in their group. We compare this environment to one in which only one group is exogenously endowed with sanctioning institutions. We find that subjects' ability to vote on institutions leads to (i) a more efficient partition of subjects between groups, (ii) a lower migration rate, (iii) an increase in overall payoffs, and (iv) a decrease in both inter- and intra-groups (payoff) inequality. Over time, subjects tend to vote for sanctioning institutions and contribute to the public good. |
| Keywords: | Formal Sanctions, Cooperation, Migration, Voting, Experiment. |
| JEL: | C73 C91 C92 D72 H41 H73 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:1702&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Francisco Castro (Graduate School of Business, Columbia University); Gabriel Weintraub (Graduate School of Business, Stanford University) |
| Abstract: | We study the classic sequential screening problem under ex-post participation constraints. Thus the seller is required to satisfy buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently cannot use up-front fees and instead use transaction-contingent fees. We establish when the optimal selling mechanism is static (buyers are not screened) or dynamic (buyers are screened), and obtain a full characterization of such contracts. We begin by analyzing our model within the leading case of exponential distributions with two types. We provide a necessary and sufficient condition for the optimality of the static contract. If the means of the two types are sufficiently close, then no screening is optimal. If they are sufficiently apart, then a dynamic contract becomes optimal. Importantly, the latter contract randomizes the low type buyer while giving a deterministic allocation to the high type. It also makes the low type worse-off and the high type better-off compared to the contract the seller would offer if he knew the buyer’s type. Our main result establishes a necessary and sufficient condition under which the static contract is optimal for general distributions. We show that when this condition fails, a dynamic contract that randomizes the low type buyer is optimal. |
| Keywords: | Sequential screening, Ex-post participation constraints, Static contract, Dynamic contract |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2078&r=gth |
| By: | Luke Boosey (Department of Economics, Florida State University); Philip Brookins (Max Planck Institute for Research on Collective Goods); Dmitry Ryvkin (Department of Economics, Florida State University) |
| Abstract: | We consider group contests where the number of competing groups is fixed but group sizes are uncertain. Under group-level uncertainty, when players observe the size of their own group, we show that under very general conditions the contest has a semi-symmetric equilibrium where aggregate investment is invariant with respect to group size uncertainty. In contrast, under individual-level uncertainty, when players do not observe the size of their own group, the equilibrium investment is always lower than in a symmetric group contest where the same expected group size is commonly known. The reduction in investment due to population uncertainty is stronger the larger the variance in appropriately defined relative group impacts. |
| Keywords: | group contest, stochastic group size |
| JEL: | C72 D72 D82 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:fsu:wpaper:wp2017_03_01&r=gth |
| By: | Vesely, Stepan (Department of Psychology, Norwegian University of Science and Technology); Wengström, Erik (Department of Economics, Lund University) |
| Abstract: | Outcomes in social dilemmas often have a stochastic component. We report experimental findings from public good games with both correlated and independent risk across players. We find that the presence of both types of risk prevents the decay of cooperation typically observed in the standard deterministic public good game. The results further suggest that it is greater relative importance of social norms or warm glow giving, rather than risk sharing opportunities that foster cooperation in our stochastic public good game. |
| Keywords: | risk pooling; risk sharing; social norms; linear public goods game; cooperation decay; stable cooperation |
| JEL: | D03 D80 H41 |
| Date: | 2017–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2017_003&r=gth |
| By: | Bettina Klaus |
| Abstract: | For classical marriage markets with equal numbers of men and women and where all men find all women acceptable and all women find all men acceptable, Sasaki and Toda (1992) characterized the core by same-side anonymity for marriage markets, Pareto optimality, consistency, and converse consistency. Nizamogullari and Ozkal-Sanver (2014) generalized this result to the domain of classical marriage markets by adding individual rationality and replacing same-side anonymity for marriage markets with a stronger property called gender fairness. We generalize both results by characterizing the core on the domain of solvable roommate markets without so-called ``3-rings'' (and on the domain of marriage markets) by individual rationality, anonymity, Pareto optimality, consistency, and converse consistency. We also prove that extending this characterization to the domain of solvable roommate markets is not possible. |
| Keywords: | Converse Consistency, Core, Marriage and Roommate Markets |
| JEL: | C78 D63 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:17.03&r=gth |
| By: | Freeman, David; Kimbrough, Erik O.; Reiss, J. Philipp |
| Abstract: | Recent research suggests that auction winners sometimes fall prey to a "bidder's curse", paying more for an item at auction than they would have paid at a posted price. One explanation for this phenomenon is that bidders are inattentive to posted prices. We develop a model in which bidders' inattention, and subsequent overbidding, is driven by a rational response to the opportunity cost of acquiring information about the posted price. We test our model in a laboratory experiment in which subjects bid in an auction while facing an opportunity cost of looking up the posted price. We vary the opportunity cost, and we show that information acquisition decreases and consequently overbidding increases with opportunity cost as predicted. |
| Keywords: | Auctions,Bidder's Curse,Limited Attention,Experiments,Rational Ignorance |
| JEL: | C72 C92 D44 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:101&r=gth |
| By: | Jahnke, Björn; Fochmann, Martin; Wagener, Andreas |
| Abstract: | Reliable institutions - i.e., institutions that live up to the norms that agents expect them to keep - foment cooperative behavior. We experimentally confirm this hypothesis in a public goods game with a salient norm that cooperation was socially demanded and corruption ought not to occur. When nevertheless corruption attempts came up, groups that were told that "the system" had fended off the attempts made considerably higher contributions to the public good than groups that only learned that the attempt did not aect their payoffs or that were not at all exposed to corruption. |
| JEL: | H41 A13 C91 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc16:145646&r=gth |
| By: | Rabah Amir; Sergei Belkov; Igor V. Evstigneev |
| Abstract: | We analyze the concept of correlated equilibrium in the framework of two-player two-strategy games. This simple framework makes it possible to clearly demonstrate the characteristic features of this concept. We develop an intuitive and easily memorizable test for equilibrium conditions and provide a complete classification of symmetric correlated equilibria in symmetric games. |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:man:sespap:1706&r=gth |
| By: | Krishna Dasaratha; Kevin He |
| Abstract: | We study a model of sequential learning with naive agents on a network. The key behavioral assumption is that agents wrongly believe their predecessors act based on only private information, so that correlation between observed actions is ignored. We provide a simple linear formula characterizing agents' actions in terms of paths in the network and use this formula to determine when society learns correctly in the long-run. Because early agents are disproportionately influential, standard network structures can lead to herding on incorrect beliefs. The probability of mislearning increases when link densities are higher and when networks are more integrated. When actions can only communicate limited information, segregated networks often lead to persistent disagreement between groups. |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1703.02105&r=gth |
| By: | Fausto, Cavalli; Mario, Gilli; Ahmad, Naimzada; |
| Abstract: | The purpose of this paper is to propose a symmetric two player general contest model in order to study the relationship between equilibria and crucial structural parameters of the model. In particular, given a general specification of the players’ set of possible entries, of the agents’ utility functions, and of the rules that presides over outcomes, we aim to analyze the characteristics of the set of equilibria as a function of structural characteristics of the contest technology and of the outcome function. Focusing on three main cases, we study the effect of introducing spillover in the marginal productivity of agents’ efforts and in the polarization between agents’ goals. Firstly, we show that without spillover the equilibrium efforts’ intensity is uniquely connected to the ratio between marginal productivity of effort and polarization. Secondly, we are able to connect existence of multiple symmetric and asymmetric equilibria to the intensity of spillover effects into outcomes. Finally, we show that spillover in contest technology can imply the non-existence of equilibria. |
| Keywords: | symmetric contest, multiple equilibria, symmetric and asymmetric equilibria |
| JEL: | C72 D72 D74 |
| Date: | 2017–03–03 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:364&r=gth |
| By: | Achim Voss (University of Hamburg); Mark Schopf (University of Paderborn) |
| Abstract: | The article compares two models of lobby influence on policy choice: The Grossman & Helpman (1994) contribution-schedule model and a negotiation between the lobbies and the government summarized by a Nash-bargaining function. The literature uses the models interchangeably because they imply the same equilibrium policy. We derive under which conditions they lead to the same payments, equilibrium utilities, and total efficiency. They coincide under particular assumptions about bargaining power and disagreement utility. |
| Keywords: | Nash Bargaining; Common-Agency Model; Lobbying |
| JEL: | C71 C78 D72 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:dispap:27&r=gth |
| By: | Schumacher, Heiner; Karle, Heiko; Volund, Rune |
| Abstract: | We analyze how early settlement offers affect Nash bargaining outcomes when agents are asymmetrically informed about the distribution of bargaining powers and exhibit expectations-based loss-aversion preferences. Before the start of the bargaining process, the sender has private information about the receiver’s bargaining power. His settlement offers may convey this private information so that they change the receiver’s expectations and, by loss aversion, preferences. We show that the sender can exploit this mechanism by making non-binding settlement offers, i.e., the receiver is free to accept them at any time, even after learning her true bargaining value. |
| JEL: | C78 D03 K12 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc16:145772&r=gth |