Characterizing the Value and Effect of Perceptiveness in Various Game-Theoretic Settings
Abstract
This thesis investigates the value and effect that perceptiveness has in three game-theoretic settings. I consider a player to be expert if they know the value of a particular payoff-relevant parameter in the models I study. If the player does not know such value, I consider the player to be inexpert. A player is perceptive if they know with certainty whether their opponent is expert. Otherwise, the player is imperceptive. The goal of this thesis is to provide insight regarding the potential value and effect that perceptiveness has in the game-theoretic settings I study.
The first model I consider emulates a two-player, one-round game of poker. The second model I investigate is a two-player market-entry game. The third model I study depicts a two-player market-entry game that is influenced by an information designer who aims to maximize producer surplus. In each model, I consider distinct information structures, which vary in terms of the players' levels of expertise and perceptiveness. In the first two models, I solve for the Bayesian Nash equilibria of each game and compute each agent's expected payoff. Then, by comparing the equilibrium action and expected payoff of an agent when perceptive to that when imperceptive, holding all else constant, I determine the agent's value of perceptiveness and the effect that perceptiveness has on the agent's equilibrium strategy. In the third model, I solve for the information designer's attainable decision rules, then determine which of the attainable decision rules maximizes producer surplus.
Among other insights, I find that perceptiveness is generally valuable, whether that be from the perspective of a poker player, a player considering market-entry, or an information designer in a market-entry game. Furthermore, under an equilibrium that treats the market-entry players as symmetrically as possible, the value of perceptiveness is positive when both players have a sufficiently high probability of being expert; whereas, the value of perceptiveness is zero when either player is inexpert with a sufficiently high probability. Also, perceptiveness is generally less beneficial to players considering market entry than it is to players playing poker.