Choice of Prizes Allocated by Multiple Lotteries with Endogenously Determined Probabilities

We study a class of interactive decision making situations in which each agent must choose to participate in one of several lotteries with commonly known prizes. In contrast to the widely studied paradigm of choice between gambles in individual decision making under risk, the probability of winning a prize in each of the lotteries in our study is endogenously determined. In particular, for each lottery, it is known to decrease in the number of agents choosing to play that lottery. We construct the Nash equilibrium solution to this game and then test it experimentally in the special case where each lottery yields only a single prize. The results show a remarkable degree of tacit coordination that supports the equilibrium solution under the assumption of common risk-aversion. However, this coordination is not achieved via individual level randomization. Rather, the entry decisions of most of the subjects can be characterized by local adjustments to the outcome of the previous iteration of the same game along the lines suggested by anticipatory learning models.