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on Game Theory |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Juuso Valimaki (Dept. of Economics, Helsinki School of Economics) |
| Abstract: | We consider truthful implementation of the socially efficient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satisfied for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and efficient exit conditions. We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. We show that the dynamic pivot mechanism is equivalent to a modified second price auction. |
| Keywords: | Pivot mechanisms, Dynamic mechanism design, Ex-post equilibrium, Marginal contribution, Multi-armed bandit, Bayesian learning |
| JEL: | C72 C73 D43 D83 |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1672&r=gth |
| By: | Steven A. Matthews (Department of Economics, University of Pennsylvania) |
| Abstract: | This paper studies a class of dynamic voluntary contribution games in a setting with discounting and neoclassical payoffs (differentiable, strictly concave in the public good, and quasilinear in the private good). An achievable profile is the limit point of a subgame perfect equilibrium path -- the ultimate cumulative contribution vector of the players. A profile is shown to be achievable only if it is in the undercore of the underlying coalitional game, i.e., the profile cannot be blocked by a coalition using a component-wise smaller profile. Conversely, if free-riding incentives are strong enough that contributing zero is a dominant strategy in the stage games, then any undercore profile is the limit of achievable profiles as the period length shrinks. Thus, in this case when the period length is very short, (i) the set of achievable contributions does not depend on whether the players can move simultaneously or only in a round-robin fashion; (ii) an efficient profile can be approximately achieved if and only if it is in the core of the underlying coalitional game; and (iii) any achievable profile can be achieved almost instantly. |
| Keywords: | dynamic games, monotone games, core, public goods, voluntary contribution, gradualism |
| JEL: | C7 |
| Date: | 2008–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-028&r=gth |
| By: | Fehr, Dietmar (Technical University of Berlin); Kübler, Dorothea (Technical University of Berlin); Danz, David N. (Technical University of Berlin) |
| Abstract: | We study beliefs and choices in a repeated normal-form game. In addition to a baseline treatment with common knowledge of the game structure and feedback about choices in the previous period, we run treatments (i) without feedback about previous play, (ii) with no information about the opponent’s payoffs and (iii) with random matching. Using Stahl and Wilson’s (1995) model of limited strategic reasoning, we classify behavior with regard to its strategic sophistication and consider its development over time. We use belief statements to check for the consistency of subjects’ actions with the stated beliefs as well as for the accuracy of their beliefs (relative to the opponent’s true choice). In the baseline treatment we observe more sophisticated play as well as more accurate beliefs and more best responses to beliefs over time. We isolate feedback as the main driving force of learning to play strategically and to form beliefs that accurately predict the behavior of the opponent. |
| Keywords: | beliefs, experiments, strategic uncertainty, learning |
| JEL: | C72 C92 D84 |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp3627&r=gth |
| By: | Klein, Nicolas; Rady, Sven |
| Abstract: | We analyze a two-player game of strategic experimentation with two-armed bandits. Each player has to decide in continuous time whether to use a safe arm with a known payoff or a risky arm whose likelihood of delivering payoffs is initially unknown. The quality of the risky arms is perfectly negatively correlated between players. In marked contrast to the case where both risky arms are of the same type, we find that learning will be complete in any Markov perfect equilibrium if the stakes exceed a certain threshold, and that all equilibria are in cutoff strategies. For low stakes, the equilibrium is unique, symmetric, and coincides with the planner's solution. For high stakes, the equilibrium is unique, symmetric, and tantamount to myopic behavior. For intermediate stakes, there is a continuum of equilibria. |
| Keywords: | Strategic Experimentation; Two-Armed Bandit; Exponential Distribution; Poisson Process; Bayesian Learning; Markov Perfect Equilibrium |
| JEL: | C73 D83 H41 O32 |
| Date: | 2008–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:5332&r=gth |
| By: | Said, Maher |
| Abstract: | We develop a model of a dynamic market with randomly arriving participants. Both buyers and sellers arrive probabilistically over time. The valuation of each buyer for each object is independently distributed and private information to each buyer. Equilibrium prices are determined by a sequence of second-price auctions. We examine the manner in which equilibrium behavior and payoffs are influenced by both current market conditions and anticipated future dynamics. |
| Keywords: | Dynamic markets; Random arrivals; Endogenous option value; Sequential auctions; Stochastic equivalence. |
| JEL: | D44 D83 C73 |
| Date: | 2008–08–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:9868&r=gth |
| By: | Adam Brandenburger |
| Date: | 2008–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:122247000000002312&r=gth |
| By: | Evrenk, Haldun (Suffolk University, Department of Economics) |
| Abstract: | We study the Nash Equilibrium of three-candidate unidimensional spatial competition when candidates differ in their non-policy characteristics (valence). If the voters' policy preferences are represented by a strictly convex loss function, and if the voter density is unimodal and symmetric, then a unique, modulo symmetry, local Nash Equilibrium exists under fairly plausible conditions. The global Nash Equilibrium, however, exists when only one candidate has a valence advantage (or disadvantage) while the other two candidates have the same valence |
| Keywords: | Multi-candidate competition; valence; local Nash Equilibrium |
| JEL: | C72 H89 |
| Date: | 2008–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:suf:wpaper:2008-2&r=gth |