124,458 research outputs found

    A Theory of Sequential Reciprocity

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    Many experimental studies indicate that people are motivated by reciprocity. Rabin (1993) develops techniques for incorporating such concerns into game theory and economics. His model, however, does not fare well when applied to situations with an interesting dynamic structure (like many experimental games), because it is developed for normal form games in which information about the sequential structure of a strategic situation is suppressed. In this paper we develop a theory of reciprocity for extensive games in which the sequential structure of a strategic situation is made explicit. We propose a new solution concept‚ÄĒ sequential reciprocity equilibrium‚ÄĒwhich is applicable to extensive games, and we prove a general equilibrium existence result. The model is applied in several examples, including some well known experimental games like the Ultimatum game and the Sequential Prisoners‚Äô Dilemma.Reciprocity;extensive games

    Sequential Parimutuel Games.

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    In a parimutuel betting system, a successful player's return depends on the number of players who choose the same action. This paper examines a general solution for two-action sequential parimutuel games, and shows how the (unique) equilibrium of such games leads to a simple pattern of behaviour. In particular, we show that there is an advantage to being an early mover, that early players might choose actions with an ex ante low probability of success, and that player action choices can 'flip' with small changes in the parameters of the game.GAME THEORY ; INVESTMENTS

    Algorithms and Conditional Lower Bounds for Planning Problems

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    We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set, and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.Comment: Accepted at ICAPS'1

    Complete Sequential Equilibrium and Its Alternative

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    We propose a complete version of the sequential equilibrium (CSE) and its alternative solution concept (WCSE) for general finite-period games with observed actions. The sequential equilibrium (SE) is not a complete solution concept in that it might not be a Nash equilibrium in the general games that allow a continuum of types and strategies. The CSE is always a Nash equilibrium and is equivalent to the SE in finite games. So, the CSE is a complete solution concept in the general games as a version of the SE. The WCSE is a weak, but simple version of the CSE. It is also a complete solution concept and functions as an alternative solution concept to the CSE. Their relation with converted versions of the perfect equilibrium and the perfect Bayesian equilibrium are discussedComplete Belief, Complete Sequential Equilibirum, Finite-period game, Solution Concept, Sequential Convergency, Sequential Equilibrium.

    Existence of Equilibrium in Common Agency Games with Adverse Selection

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    We establish the existence of sequential equilibria in general menu games, known to be sufficient to analyze common agency problems. In particular, we show that our result solves some unpleasant features of early approaches.Common Agency, Menu Games, Sequential Equilibrium

    Estimating Sequential-move Games by a Recursive Conditioning Simulator

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    Sequential decision-making is a noticeable feature of strategic interactions among agents. The full estimation of sequential games, however, has been challenging due to the sheer computational burden, especially when the game is large and asymmetric. In this paper, I propose an estimation method for discrete choice sequential games that is computationally feasible, easy-to-implement, and e¬Ę cient, by modifying the Geweke-Hajivassiliou-Keane (GHK) simulator, the most widely used probit simulator. I show that the recursive nature of the GHK simulator is easily dovetailed with the sequential structure of strategic interactions.

    Negative results in the theory of games with lexicographic utilities

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    When players may have lexicographic utilities, there are: (i) extensive games having a non-empty set of equilibria but empty sets of sequentially rational, sequential and perfect equilibria (ii) normal form games having a non-empty set of equilibria but an empty set of proper equilibria and no stable set of equilibria and (iii) two extensive games having the same normal form representation and disjoint sets of sequential equilibria.lexicographic expected utility
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