A Bayesian Sequential Experimental Study of Learning in Games

Abstract We apply a sequential Bayesian sampling procedure to study two models of learning in repeated games. In the first model individuals learn only about an opponent when they play her or him repeatedly but do not update from their experience with that opponent when they move on to play the same game with other opponents. We label this the nonsequential model. In the second model individuals use Bayesian updating to learn about population parameters from each of their opponents, as well as learning about the idiosyncrasies of that particular opponent. We call this the sequential model. We sequentially sample observations on the behavior of experimental subjects in the so-called “centipede game.” This game allows for a trade-off between competition and cooperation, which is of interest in many economic situations. At each point in time, the “state” of our dynamic problem consists of our beliefs about the two models and beliefs about the nuisance parameters of the two models. Our “choice” set is to samp...

[1]  John H. Miller,et al.  Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence , 1993 .

[2]  J. Kiefer,et al.  Asymptotically Optimum Sequential Inference and Design , 1963 .

[3]  Nimrod Megiddo,et al.  Research REMARKS ON BOUNDED RATIONALITY , 1986 .

[4]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[5]  Richard T. Boylan,et al.  Fictitious Play: A Statistical Study of Multiple Economic Experiments , 1993 .

[6]  Colin Camerer,et al.  EXPERIMENTAL TESTS OF A SEQUENTIAL EQUILIBRIUM REPUTATION MODEL , 1988 .

[7]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[8]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[9]  H. Chernoff.  Sequential Design of Experiments , 1959 .

[10]  G. Lorden.  Nearly-optimal sequential tests for finitely many parameter values , 1977 .

[11]  Ken Binmore,et al.  Modeling rational players I , 1987 .

[12]  P. Reny.  Backward Induction, Normal Form Perfection and Explicable Equilibria , 1992 .

[13]  R. Selten.  Evolutionary stability in extensive two-person games , 1983 .

[14]  J. Harsanyi.  Games with Incomplete Information Played by “Bayesian” Players Part II. Bayesian Equilibrium Points , 1968 .

[15]  H. Chernoff.  Sequential Analysis and Optimal Design , 1987 .

[16]  Philip J. Reny,et al.  BACKWARD INDUCTION, NORMAL FORM PERFECTION , 1992 .

[17]  A. N. Sirjaev,et al.  Statistical Sequential Analysis , 1973 .

[18]  R. McKelvey,et al.  An experimental study of the centipede game , 1992 .

[19]  R. Rosenthal.  Games of perfect information, predatory pricing and the chain-store paradox , 1981 .