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on Game Theory |
| By: | Giuseppe Cappelletti (Bank of Italy) |
| Abstract: | Rationalizability is a widely accepted solution concept in the study of strategic form game with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality. Battigalli and Siniscalchi extend rationalizability and derive the solution concept called Δ-rationalizability. Their analysis is based on the following assumptions: (a) players are rational; (b) their first-order beliefs satisfy some restrictions; and (c) there is common belief of (a) and (b). In this note I focus on games with complete information and I characterize Δ-rationalizability with a new notion of iterative dominance which is able to capture the additional hypothesis on players' beliefs. |
| Keywords: | rationalizability, strategic form game, complete information |
| JEL: | C72 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_757_10&r=gth |
| By: | Onur Kesten (Carnegie Mellon University); M. Utku Ünver (Boston College) |
| Abstract: | A new centralized mechanism was introduced in New York City and Boston to assign students to public schools in district school-choice programs. This mechanism was advocated for its superior fairness property, besides others, over the mechanisms it replaced. In this paper, we introduce a new framework for investigating school-choice matching problems and two ex-ante notions of fairness in lottery design, strong ex-ante stability and ex-ante stability. This frame- work generalizes known one-to-many two-sided and one-sided matching models. We first show that the new NYC/Boston mechanism fails to satisfy these fairness properties. We then propose two new mechanisms, the fractional deferred-acceptance mechanism, which is ordinally Pareto dominant within the class of strongly ex-ante stable mechanisms, and the fractional deferred- acceptance and trading mechanism, which satisfies equal treatment of equals and constrained ordinal Pareto efficiency within the class of ex-ante stable mechanisms. |
| Keywords: | Matching, School Choice, Deferred Acceptance, Stability, Ordinal Efficiency, Market Design |
| JEL: | C71 C78 D71 D78 |
| Date: | 2010–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:737&r=gth |
| By: | Takashi Kunimoto; Roberto Serrano |
| Abstract: | Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions cannot be dispensed with. We term the condition “restricted deceptionproofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation are more restrictive than previously thought. |
| Keywords: | mechanism design; exact and approximate implementation; iteratively undominated strategies; restricted deception-proofness; incentive compatibility; measurability |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2010-2&r=gth |
| By: | Geoffroy de Clippel; David Perez-Castrillo; David Wettstein |
| Abstract: | We propose a definition of egalitarian equivalence that extends Pazner and Schmeidler’s (1978) concept to environments with incomplete information. If every feasible allocation rule can be implemented by an incentive compatible mechanism (as, for instance, in the case of non-exclusive information), then interim egalitarian equivalence and interim incentive efficiency remain compatible, as they were under complete information. When incentive constraints are more restrictive, on the other hand, the two criteria may become incompatible. |
| Keywords: | Pareto Efficiency: Egalitarian Equivalence; Asymmetric Information |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2010-5&r=gth |
| By: | Francisco J. Santos-Arteaga (Universidad Complutense de Madrid,Instituto Complutense de Estudios Internacionales (ICEI)) |
| Abstract: | The literature on bank runs reduces all coordination mechanisms triggering attacks on banks to exogenous sunspots. We present a general equilibrium version of these models where the uncertainty faced by depositors is modeled explicitly, such that bank runs arise as optimal equilibrium outcomes corresponding to Bayesian coordination games played by rational agents before depositing. Differentials in information sets between the bank and its depositors lead to rational self-contained equilibrium runs. The coexistence of different beliefs in equilibrium jointly with the self-fulfilling nature of the attacks follow from Adam Smith's invisible hand principle. The runs obtained do not violate the revelation principle. |
| Keywords: | Bank runs, Self-contained attacks, Bayesian coordination games, Revelation principle, Invisible hand principle, Pánicos bancarios, Ataques autocontenidos, Juegos de coordinación Bayesianos, Principio de revelación, Principios de la mano invisible. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:wpaper:02-10&r=gth |
| By: | Tamás Kovács; Marc Willinger |
| Abstract: | We provide new evidence about a positive correlation between the own amount sent and the own amount returned in the investment game. Our analysis relies on experimental data collected under the strategy method for establishing our main result. While the percentage returned is independent of the amount received for most of our subjects, it is strongly correlated to their amount sent as a trustor. Our analysis is based on a two-way classification of subjects : according to their trusting type and according to their reciprocal type. We show the existence of a strong correlation between trusting types and reciprocal types within subjects. |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:10-03&r=gth |