Regret Minimizing Equilibria and Mechanisms for Games with Strict Type Uncertainty (1207.4147v1)

Abstract: Mechanism design has found considerable application to the construction of agent-interaction protocols. In the standard setting, the type (e.g., utility function) of an agent is not known by other agents, nor is it known by the mechanism designer. When this uncertainty is quantified probabilistically, a mechanism induces a game of incomplete information among the agents. However, in many settings, uncertainty over utility functions cannot easily be quantified. We consider the problem of incomplete information games in which type uncertainty is strict or unquantified. We propose the use of minimax regret as a decision criterion in such games, a robust approach for dealing with type uncertainty. We define minimax-regret equilibria and prove that these exist in mixed strategies for finite games. We also consider the problem of mechanism design in this framework by adopting minimax regret as an optimization criterion for the designer itself, and study automated optimization of such mechanisms.

• The paper introduces a novel minimax regret criterion to address strict type uncertainty without relying on probabilistic models.
• It defines minimax-regret equilibria in mixed strategies for finite games, ensuring a worst-case performance guarantee.
• It extends mechanism design by incorporating automated optimization to minimize worst-case regret in uncertain environments.

The paper "Regret Minimizing Equilibria and Mechanisms for Games with Strict Type Uncertainty" addresses a novel approach to mechanism design in situations where type uncertainty among agents is not easily quantified. Traditionally, in games of incomplete information, a probabilistic view is taken to model the uncertainty of an agent's type, such as their utility functions. However, this paper explores scenarios where such quantification is challenging or impossible.

Key Contributions:

1. Strict Type Uncertainty: The authors focus on settings where agents and mechanism designers cannot quantify uncertainty over types, which is a common real-world complexity. This differs from the typical probabilistic assumptions, making the research applicable to more realistic scenarios.
2. Minimax Regret Criterion: The core innovation of the paper is the adoption of the minimax regret criterion in this context. The minimax regret approach is a robust decision-making framework that does not require probabilistic assumptions about type distributions. It focuses on minimizing the maximum possible regret an agent or designer might experience, providing a worst-case guarantee that is attractive in uncertain environments.
3. Minimax-Regret Equilibria: The authors define equilibria based on the minimax regret criterion and prove that such equilibria exist in mixed strategies for finite games. This is a significant theoretical contribution, showing that players can still reach a form of stability without relying on probability-based models.
4. Mechanism Design: The paper extends the minimax regret approach to the design of mechanisms themselves. By doing so, the mechanism designer seeks to minimize their own worst-case regret, optimizing the mechanism for environments with strict type uncertainty.
5. Automated Optimization: The authors also investigate automating the optimization of such mechanisms, suggesting that computational methods could be employed to efficiently design mechanisms under this framework.

Implications:

The introduction of minimax-regret equilibria provides an alternative framework for games with type uncertainty that does not rely on probability. This is particularly relevant for complex environments like economic markets or automated systems where agent preferences might be unknown or unquantifiable. The robustness offered by the minimax regret criterion could improve decision-making processes in these uncertain environments. Additionally, the paper's approach to mechanism design has implications for developing new protocols for agent interactions where traditional methods fall short due to the lack of precise information.