Creator: Bryant, John B. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 175 Abstract:
Game theory is both at the heart of economics and without a definitive solution. This paper proposes a solution. It is argued that a dominance criterion generates a, and perhaps the, generalized equilibrium solution for game theory. First we provide a set theoretic perspective from which to view game theory, and then present and discuss the proposed solution.
Keyword: Nash equilbrium, Dominance, and Equilibria Subject (JEL): C72 - Noncooperative Games, C68 - Computable General Equilibrium Models, and C70 - Game Theory and Bargaining Theory: General
Creator: Turdaliev, Nurlan Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 596 Abstract:
In a repeated game of incomplete information, myopic players form beliefs on next-period play and choose strategies to maximize next-period payoffs. Beliefs are treated as forecast of future plays. Forecast accuracy is assessed using calibration tests, which measure asymptotic accuracy of beliefs against some realizations. Beliefs are calibrated if they pass all calibration tests. For a positive Lebesgue measure of payoff vectors, beliefs are not calibrated. But, if payoff vector and calibration test are drawn from a suitable product measure, beliefs pass the calibration test almost surely.
Subject (JEL): C10 - Econometric and Statistical Methods and Methodology: General, C70 - Game Theory and Bargaining Theory: General, and C72 - Noncooperative Games
Creator: Cole, Harold Linh, 1957-, Mailath, George Joseph, and Postlewaite, A. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 253 Abstract:
This paper addresses the question of whether agents will invest efficiently in attributes that will increase their productivity in subsequent matches with other individuals. We present a two-sided matching model in which buyers and sellers make investment decisions prior to a matching stage. Once matched, the buyer and seller bargain over the transfer price. In contrast to most matching models, preferences over possible matches are affected by decisions made before the matching process. We show that if bargaining respects the existence of outside options (in the sense that the resulting allocation is in the core of the assignment game), then efficient decisions can always be sustained in equilibrium. However, there may also be inefficient equilibria. Our analysis identifies a potential source of inefficiency not present in most matching models.
Keyword: Matching models, Hold-up problems, Investment, and Contracting Subject (JEL): C70 - Game Theory and Bargaining Theory: General, D52 - Incomplete Markets, and D20 - Production and Organizations: General
Creator: Blume, Andreas and Franco, April Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 299 Abstract:
We study decentralized learning in organizations. Decentralization is captured through a symmetry constraint on agents’ strategies. Among such attainable strategies, we solve for optimal and equilibrium strategies. We model the organization as a repeated game with imperfectly observable actions. A fixed but unknown subset of action profiles are successes and all other action profiles are failures. The game is played until either there is a success or the time horizon is reached. For any time horizon, including infinity, we demonstrate existence of optimal attainable strategies and show that they are Nash equilibria. For some time horizons, we can solve explicitly for the optimal attainable strategies and show uniqueness. The solution connects the learning behavior of agents to the fundamentals that characterize the organization: Agents in the organization respond more slowly to failure as the future becomes more important, the size of the organization increases and the probability of success decreases.
Keyword: Decentralized Learning, Organizations, and Game Theory Subject (JEL): C70 - Game Theory and Bargaining Theory: General and D21 - Firm Behavior: Theory
Creator: Bryant, John B. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 144 Keyword: Multiple equilibria, Game, Nash equilibrium, and Minimax Subject (JEL): D50 - General Equilibrium and Disequilibrium: General and C70 - Game Theory and Bargaining Theory: General