Thesis Format

Integrated Article

Characterizing the Value and Effect of Perceptiveness in Various Game-Theoretic Settings

Terrence Adam Rooney, The University of Western OntarioFollow

Degree

Doctor of Philosophy

Program

Economics

Supervisor

Streufert, Peter A.

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.

Summary for Lay Audience

This thesis studies the value and effect that perceptiveness has in three game-theoretic settings. I consider a player to be expert if they can discern their likelihood of realizing a high payoff in a strategic setting. If the player cannot discern such, 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 a third player that can signal to the other two players whether they should enter the market. The third player aims to maximize the combined well-being of the two other players. In each model, I consider distinct endowments of information between the players. These endowments vary in terms of the players' expertise and perceptiveness. By obtaining the solutions and expected payoffs of a player when they are perceptive, then comparing such to that when the player is imperceptive, I determine the player's value of perceptiveness and the effect that perceptiveness has on the player's strategy. In the third model, I solve for the attainable signals the third player can send, then determine which signal maximizes the combined well-being of the other two players.

Among other insights, I find that perceptiveness is generally valuable in all three models. Furthermore, using a solution 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. I also find that perceptiveness is generally less beneficial to players considering market entry than it is to players playing poker.

Recommended Citation

Rooney, Terrence Adam, "Characterizing the Value and Effect of Perceptiveness in Various Game-Theoretic Settings" (2020). Electronic Thesis and Dissertation Repository. 7256.
https://ir.lib.uwo.ca/etd/7256