Game theory: analysis of confllict

Abstract

Game theory provides a unified mathematical framework for analyzing conflict and cooperation between intelligent, rational decision-makers. Grounded in Bayesian decision theory and the expected-utility maximization theorem, the discipline models interactions using strategic, extensive, and Bayesian forms to address varying levels of information and timing. Fundamental solution concepts, primarily the Nash equilibrium and its refinements—such as sequential, perfect, and proper equilibria—identify stable patterns of behavior by accounting for off-equilibrium path incentives and the role of common knowledge. Analysis extends to repeated games, where folk theorems demonstrate how long-term relationships sustain cooperative outcomes through reciprocity and reputation, even under conditions of imperfect monitoring. The scope further encompasses cooperative game theory, focusing on coalitional stability and equitable bargaining outcomes through concepts such as the core and the Shapley value. This analytical approach integrates noncooperative foundations with coalitional analysis to address mechanism design and collective-choice problems under uncertainty. By examining the structural constraints of communication and private information, these models elucidate how rational agents reach agreements, distribute surplus, and manage conflict in complex social and economic systems. – AI-generated abstract.