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on Game Theory |
| By: | Duersch, Peter; Oechssler, Jörg; Schipper, Burkhard C. |
| Abstract: | It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies. |
| Keywords: | Symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity. |
| JEL: | C73 C72 |
| Date: | 2010–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0500&r=gth |
| By: | Anat Bracha (Federal Reserve Bank of Boston); Donald J. Brown (Department of Economics, Yale University) |
| Abstract: | Optimism-bias is inconsistent with the independence of decision weights and payoffs found in models of choice under risk, such as expected utility theory and prospect theory. Hence, to explain the evidence suggesting that agents are optimistically biased, we propose an alternative model of risky choice, affective decision-making, where decision weights -- which we label affective or perceived risk -- are endogenized. Affective decision making (ADM) is a strategic model of choice under risk, where we posit two cognitive processes: the "rational" and the "emotional" processes. The two processes interact in a simultaneous-move intrapersonal potential game, and observed choice is the result of a pure strategy Nash equilibrium in this potential game. We show that regular ADM potential games have an odd number of locally unique pure strategy Nash equilibria, and demonstrate this finding for affective decision making in insurance markets. We prove that ADM potential games are refutable, by axiomatizing the ADM potential maximizers. |
| Keywords: | Affective decision-making, Optimism-bias, ADM potential games, Demand for insurance |
| JEL: | D01 D81 G22 |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1759&r=gth |
| By: | Andersson, Ola (Dept. of Economics, Stockholm School of Economics); Argenton, Cédric (Tilburg University); Weibull, Jörgen (Dept. of Economics, Stockholm School of Economics) |
| Abstract: | We model a player's uncertainty about other player's strategy choices as probability distributions over their strategy sets. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in each of which every player's strategy is optimal under his or her uncertainty about the pthers. We apply this definition to Bertrand games with a continuum of equilibrium prices and show that our robustness criterion selects a unique Nash equilibrium price. This selection agrees with available experimental findings. |
| Keywords: | Nash equilibrium; refinement; strategic uncertainty; price competition |
| JEL: | C72 D43 L13 |
| Date: | 2010–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0726&r=gth |
| By: | Duersch, Peter; Oechssler, Jörg; Schipper, Burkhard C. |
| Abstract: | We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent. |
| Keywords: | Imitate-the-best; learning; symmetric games; relative payoffs; zero- sum games. |
| JEL: | C72 C73 D43 |
| Date: | 2010–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0499&r=gth |
| By: | Estrada, Fernando |
| Abstract: | In their recent work Thomas S. Schelling (2007, 2010), reiterating original arguments about game theory and its applications to social sciences. In particular, game theory helps to explore situations in which agents make decisions interdependent (strategic communication). Schelling's originality is to extend economic theory to social sciences. When a player can anticipate the options and influence the decisions of others. The strategy, indirect communication plays a crucial role. To illustrate, we investigate how to perform the payoff matrix in cases of bribery and threat |
| Keywords: | Social Science; Schelling; game theory; strategic communications; bribes; threats. |
| JEL: | B0 D81 A1 D82 C70 C7 B00 D84 D7 D8 D80 C72 |
| Date: | 2010–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:21772&r=gth |
| By: | Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Maria Romaniello (Seconda Università di Napoli) |
| Abstract: | We consider pure exchange economies with finitely many private goods involving the choice of a public project. We discuss core-equivalence results in the general framework of non-Euclidean representation of the collective goods. We define a contribution scheme to capture the fraction of the total cost of providing the project that each blocking coalition is expected to cover. We show that for each given contribution scheme defined over the wider class of Aubin coalitions, the resulting core is equivalent to the corresponding linear cost share equilibria. We also characterize linear cost share equilibria in terms of the veto power of the grand coalition. It turns out that linear cost share equilibria are exactly those allocations that cannot be blocked by the grand coalition with reference to auxiliary economies with the same space of agents and modified initial endowments and cost functions. Unlike the Aubin-type equivalence, this characterization does not depend on a particular contribution scheme. |
| Keywords: | Public project, cost share equilibrium, core, non-dominated allocation, grand coalition |
| JEL: | D51 D60 H41 |
| Date: | 2010–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:248&r=gth |
| By: | Takashi Kunimoto (McGill University and CIREQ); Roberto Serrano (Brown University and IMDEA Ciencias Sociales) |
| Abstract: | We assess the strength of the different conditions identified in the literature of robust mechanism design. We focus on three conditions: ex post incentive compatibility, robust monotonicity, and robust measurability. Ex post incentive compatibility has been shown to be necessary for any concept of robust implementation, while robust monotonicity and robust measurability have been shown to be necessary for robust (full) exact and virtual implementation, respectively. This paper shows that while violations of ex post incentive compatibility and robust monotonicity do not easily go away, we identify a mild condition on environments in which robust measurability is satisfied by all social choice functions over an open and dense subset of first-order types. We conclude that there is a precise sense in which robust virtual implementation can be significantly more permissive than robust exact implementation. |
| Keywords: | robust mechanism design; ex post incentive compatibility; robust monotonicity; robust measurability |
| JEL: | C72 D78 D82 |
| Date: | 2010–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2010-05&r=gth |
| By: | Dimitrios Diamantaras (Department of Economics, Temple University); Robert P. Gilles (Management School, Queen’s University) |
| Abstract: | In this paper we argue that ambiguity, combined with social opinion formation can be represented as part of a game-theoretic equilibrium concept that transcends the standard Nash equilibrium concept, applied to a model of the tragedy of the commons. Our modeling can shed some light on the international environment crisis and the relevant ongoing international negotiations. We conclude that social opinion formation in most cases has a significant impact on equilibrium common property resource usage. |
| Keywords: | Externalities, environment, ambiguity, ambiguity equilibrium |
| JEL: | C72 D62 D81 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:tem:wpaper:1006&r=gth |
| By: | Carlos Scartascini; Mariano Tommasi; Ernesto Stein |
| Abstract: | The capacity to sustain policies over time and the capacity to adjust policies in the face of changing circumstances are two desirable properties of policymaking systems. The veto player approach has suggested that polities with more veto players will have the capacity to sustain policies at the expense of the ability to change policy when necessary. This paper disputes that assertion from an intertemporal perspective, drawing from transaction cost economics and repeated game theory and showing that some countries might have both more credibility and more adaptability than others. More generally, the paper argues that, when studying the effects of political institutions on policy outcomes, a perspective of intertemporal politics might lead to predictions different from those emanating from more a-temporal approaches. |
| Keywords: | Political institutions, Public policies, Veto players, Policy adaptability, Policy stability, Intertemporal, Credibility, Repeated games |
| JEL: | D72 D78 H10 H50 |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:idb:wpaper:4660&r=gth |