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on Game Theory |
| By: | Dmitry Levando (National Research University Higher School of Economics) |
| Abstract: | Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This paper suggests an approach to this problem in the framework of a non-cooperative game theory. Definition of a suggested game includes a family of nested simultaneous non-cooperative finite games with intra- and inter-coalition externalities. In this family, games differ by the size of maximum coalition, partitions and by coalition structure formation rules. A result of every game consists of partition of players into coalitions and a payoff profile for every player. Every game in the family has an equilibrium in mixed strategies with possibly more than one coalition. The results of the game differ from those conventionally discussed in cooperative game theory, e.g. the Shapley value, strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. We discuss the following applications of the new game: cooperation as an allocation in one coalition, Bayesian game, stochastic games and construction of a non-cooperative criterion of coalition structure stability for studying focal points |
| Keywords: | Non-cooperative Games; Nash equilibrium; Shapley value; strong equilibrium; core |
| JEL: | C71 C72 C73 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:17015r&r=gth |
| By: | Ludovic Alexandre Julien |
| Abstract: | In this paper, we consider a sequential bilateral oligopoly market which embodies a finite number of leaders and followers who compete on quantities. We define a noncooperative equilibrium concept for this two-stage market game with complete and perfect information, namely the Stackelberg-Nash equilibrium (SNE). Then, we study the existence of a SNE with trade. The existence proof requires some steps as this market game displays a rich set of strategic interactions. In particular, to show the existence of a pure strategy subgame perfect Nash equilibrium, we have to determine the conditions under which there exist well defined continuously differentiable best responses. Some examples buttress the approach and discuss the assumptions made on the primitives. |
| Keywords: | Best responses, Stackelberg-Nash equilibrium, trade, autarky. |
| JEL: | C72 D51 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2017-22&r=gth |
| By: | Marco Pangallo; Torsten Heinrich; J Doyne Farmer |
| Abstract: | Game theory often assumes rational players that play equilibrium strategies. But when the players have to learn their strategies by playing the game repeatedly, how often do the strategies converge? We analyze generic two player games using a standard learning algorithm, and also study replicator dynamics, which is closely related. We show that the frequency with which strategies converge to a fixed point can be understood by analyzing the best reply structure of the payoff matrix. A Boolean transformation of the payoff matrix, replacing all best replies by one and all other entries by zero, provides a reasonable approximation of the asymptotic strategic dynamics. We analyze the generic structure of randomly generated payoff matrices using combinatorial methods to compute the frequency of cycles of different lengths under the microcanonical ensemble. For a game with $N$ possible moves the frequency of cycles and non-convergence increases with $N$, becoming dominant when $N > 10$. This is especially the case when the interactions are competitive. |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1704.05276&r=gth |
| By: | Kene Boun My (BETA - University of Strasbourg, 61 avenue de la Forˆet Noire - 67085 Strasbourg Cedex); Camille Cornand (Univ Lyon, CNRS, GATE L-SE UMR 5824, F-69130 Ecully, France); Rodolphe Dos Santos Ferreira (BETA-Strasbourg University, 61 avenue de la Forêt Noire - 67085 Strasbourg Cedex, France; Catolica Lisbon School of Business and Economics) |
| Abstract: | In Keynes’ beauty contest, agents make evaluations reflecting both an expected fundamental value and the conventional value expected to be set by the market. They thus respond to fundamental and coordination motives, respectively, the prevalence of either being set exogenously. Our contribution is twofold. First, we propose a valuation game in which agents strategically choose how to weight each motive. This game emphasises public information leads agents to favour the coordination motive. Second, we test the game through a laboratory experiment. Subjects tend to conform to theoretical predictions, except when fundamental uncertainty is low relative to strategic uncertainty. |
| Keywords: | dispersed information, public information, beauty contest, coordination, experiment |
| JEL: | D84 C92 E12 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1712&r=gth |
| By: | Forges, Françoise (University of Paris-Dauphine); Horst, Ulrich (Humboldt University Berlin) |
| Abstract: | We consider generalized sender-receiver games in which the sender also has a decision to make, but this decision does not directly affect the receiver. We introduce specific perfect Bayesian equilibria, in which the players agree on a joint decision after that a message has been sent (\"talk and cooperate equilibrium\", TCE). We establish that a TCE exists provided that the receiver has a \"uniform punishment decision\" (UPD) against the sender. |
| Keywords: | sender-receiver game; commitment; cooperative solution; individual rationality; |
| JEL: | C72 C65 |
| Date: | 2017–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:17&r=gth |
| By: | Balbuzanov, Ivan (University of Melbourne); Kotowski, Maciej H. (Harvard University) |
| Abstract: | We propose a new cooperative solution for discrete exchange economies and resource allocation problems, the exclusion core. The exclusion core is neither weaker nor stronger than the (strong) core and it rests upon a foundational idea in the legal understanding of property, the right to exclude others. By reinterpreting endowments as a distribution of exclusion rights, we can extend our analysis to economies with qualified property rights and social hierarchies. The exclusion core characterizes a generalized top trading cycle algorithm in a large class of economies, including those featuring private and public ownership. |
| JEL: | C71 D47 K11 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp17-016&r=gth |
| By: | Fehr, Dietmar (University of Heidelberg); Heinemann, Frank (Technical University of Berlin); Llorente-Saguer, Aniol (Queen Mary University of London and CEPR) |
| Abstract: | This paper presents an experiment on a coordination game with extrinsic random signals, in which we systematically vary the stochastic process generating these signals and measure how signals affect behavior. We find that sunspot equilibria emerge naturally if there are salient public signals. However, highly correlated private signals can also lead to sunspot-driven behavior, even when this is not an equilibrium. Private signals reduce the power of public signals as sunspot variables. The higher the correlation of extrinsic signals and the more easily they can be aggregated, the more powerful these signals are in distracting actions from the action that minimizes strategic uncertainty. |
| Keywords: | Coordination games; strategic uncertainty; sunspot equilibria; forward guidance; expectations; |
| JEL: | C92 D82 D83 E39 E58 |
| Date: | 2017–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:11&r=gth |
| By: | Atila Abdulkadiroglu; Yeon-Koo Che; Parag A. Pathak; Alvin E. Roth; Olivier Tercieux |
| Abstract: | In 2012, New Orleans Recovery School District (RSD) became the first U.S. district to unify charter and traditional public school admissions in a single-offer assignment mechanism known as OneApp. The RSD also became the first district to use a mechanism based on Top Trading Cycles (TTC) in a real-life allocation problem. Since TTC was originally devised for settings in which agents have endowments, there is no formal rationale for TTC in school choice. In particular, TTC is a Pareto efficient and strategy-proof mechanism, but so are other mechanisms. We show that TTC is constrained-optimal in the following sense: TTC minimizes justified envy among all Pareto efficient and strategy-proof mechanisms when each school has one seat. When schools have more than one seat, there are multiple possible implementations of TTC. Data from New Orleans and Boston indicate that there is little difference across these versions of TTC, but significantly less justified envy compared to a serial dictatorship. |
| JEL: | D47 I20 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:23265&r=gth |
| By: | Hans Gersbach (ETH Zurich, Switzerland); Philippe Muller (ETH Zurich, Switzerland); Oriol Tejada (ETH Zurich, Switzerland) |
| Abstract: | We consider an infinite-horizon model of elections where policy changes are costly for citizens and parties. The so-called costs of change increase with the extent of the policy shift and make policy history-dependent. First, we provide a detailed description of the equilibrium dynamics and analyze how policies are influenced by history, costs of change, party polarization, and the incumbent's ability. We show that policies converge to a stochastic alternation between two states and that in the long run costs of change have a moderating effect on policies. Second, we analyze welfare as a function of the marginal cost of change. If the initial level of policy polarization is low, welfare is highest for intermediate marginal costs of change. Moreover, any positive level of costs of change will benefit society if the future is sufficiently valuable. If the initial level of policy polarization is high, however, welfare will be highest for low or zero costs of change. |
| Keywords: | democracy; dynamic elections; political polarization; costs of change; Markov perfect equilibrium |
| JEL: | C72 C73 D72 D78 |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:eth:wpswif:17-270&r=gth |