Strategic betting for competitive agents

In many multiagent settings, each agent's goal is to come out ahead of the other agents on some metric, such as the currency obtained by the agent. In such settings, it is not appropriate for an agent to try to maximize its expected score on the metric; rather, the agent should maximize its expected probability of winning. In principle, given this objective, the game can be solved using game-theoretic techniques. However, most games of interest are far too large and complex to solve exactly. To get some intuition as to what an optimal strategy in such games should look like, we introduce a simplified game that captures some of their key aspects, and solve it (and several variants) exactly. Specifically, the basic game that we study is the following: each agent i chooses a lottery over nonnegative numbers whose expectation is equal to its budget bi. The agent with the highest realized outcome wins (and agents only care about winning). We show that there is a unique symmetric equilibrium when budgets are equal. We proceed to study and solve extensions, including settings where agents must obtain a minimum outcome to win; where agents choose their budgets (at a cost); and where budgets are private information.

[1]  Luís M. B. Cabral,et al.  Go for Broke or Play it Safe? Dynamic Competition with Choice of Variance , 2004 .

[2]  Vincenzo Denicolò,et al.  Patent races and optimal patent breadth and length , 1996 .

[3]  Jonathan Schaeffer,et al.  Approximating Game-Theoretic Optimal Strategies for Full-scale Poker , 2003, IJCAI.

[4]  Manuela M. Veloso,et al.  Thresholded Rewards: Acting Optimally in Timed, Zero-Sum Games , 2007, AAAI.

[5]  Ilya Segal,et al.  Solutions manual for Microeconomic theory : Mas-Colell, Whinston and Green , 1997 .

[6]  Michael P. Wellman,et al.  Empirical mechanism design: methods, with application to a supply-chain scenario , 2006, EC '06.

[7]  Vincenzo Denicolò,et al.  Two-Stage Patent Races and Patent Policy , 2000 .

[8]  Luís M. B. Cabral,et al.  Increasing Dominance with No Efficiency Effect , 2000, J. Econ. Theory.

[9]  J. Laffont,et al.  Optimal auction with financially constrained buyers , 1996 .

[10]  Michael L. Littman,et al.  Abstraction Methods for Game Theoretic Poker , 2000, Computers and Games.

[11]  Michael P. Wellman,et al.  Empirical Game-Theoretic Analysis of the TAC Market Games , 2006 .

[12]  Michael R. Baye,et al.  The all-pay auction with complete information , 1990 .

[13]  Michael P. Wellman,et al.  STRATEGIC INTERACTIONS IN A SUPPLY CHAIN GAME , 2005, Comput. Intell..

[14]  Tuomas Sandholm,et al.  A Competitive Texas Hold'em Poker Player via Automated Abstraction and Real-Time Equilibrium Computation , 2006, AAAI.

[15]  All-pay auctions with budget constraints and fair insurance , 2006 .

[16]  Michael P. Wellman,et al.  An analysis of the 2004 supply chain management trading agent competition , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[17]  Dilip Mookherjee,et al.  Portfolio Choice in Research and Development , 1986 .

[18]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[19]  Luis E. Ortiz,et al.  The Penn-Lehman Automated Trading Project , 2003, IEEE Intell. Syst..

[20]  Tuomas Sandholm,et al.  Better automated abstraction techniques for imperfect information games, with application to Texas Hold'em poker , 2007, AAMAS '07.

[21]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[22]  John Collins,et al.  The Supply Chain Management Game for the 2007 Trading Agent Competition , 2004 .