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A Decision Analysis Approach to Solving the Signaling Game

Department of Economics and Business, Virginia Military Institute, Lexington, Virginia 24450
Department of Economics and Business, Virginia Military Institute, Lexington, Virginia 24450
cobbbr{at}vmi.edu
basuchoudharya{at}vmi.edu

Decision analysis has traditionally been applied to choices under uncertainty involving a single decision maker. Game theory has been applied to solving games of strategic interaction between two or more players. Building upon recent work of van Binsbergen and Marx (van Binsbergen, J. H., L. M. Marx. 2007. Exploring relations between decision analysis and game theory. Decision Anal. 4(1) 32–40), this paper defines a modified decision-theoretic approach to solving games of strategic interaction between two players. Using this method, the choices of the two players are modeled with separate decision trees comprised entirely of chance nodes. Optimal policies are reflected in the probabilities in the decision trees of each player. In many cases, the Nash equilibrium strategy for each player can be obtained by rolling back the opponent's decision tree. Results are demonstrated for the multistage signaling game, which is difficult to model using decision nodes to represent strategies, as in the approach of van Binsbergen and Marx.

Key Words: decision analysis; decision tree; game theory; mixed strategy; Nash equilibrium; signaling game
History: Received on January 22, 2009. Accepted on June 2, 2009.