Existence of Equilibria in Pure Strategies and Its Applications to Economics When the Set of Strategies is an Integer Interval

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K03553
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Economic theory
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: Watanabe Takahiro 首都大学東京, 経営学研究科, 教授 (70220895)
• Co-Investigator(Kenkyū-buntansha): 飯村 卓也 首都大学東京, 経営学研究科, 教授 (50279634)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: ゲーム理論 / 均衡の存在 / 非協力ゲーム / 純粋戦略均衡 / 離散数学

Outline of Final Research Achievements

It is known that a pure strategy equilibrium in an n-person non-cooperative game with a compact strategy set exists if the payoff function of each player is quasi-concave with respect to its own strategy and continuous in the profile of strategies． However, in the real economy, players' strategies such as price and the amount of goods are integers. The existence condition of equilibrium in such a discrete model is often not clear yet. This study examined the class and sufficient conditions of games in which a pure strategic equilibrium exists when the set of strategies is an integer interval when the strategy set is finite. We also applied this condition to an economic model in which prices and production quantities are integers, and clarified the conditions under which pure strategic equilibrium exists.

Free Research Field

ゲーム理論

Academic Significance and Societal Importance of the Research Achievements

ゲーム理論における解であるナッシュ均衡は必ず存在するという基本定理がある．しかしこの定理は，価格や生産量などの戦略変数が実数であるか，または確率を用いた混合戦略を認めるかのどちらかの必要がある．本研究では，現実の社会・経済モデルに即して(1)戦略変数が整数であり，なおかつ(2)確率を用いない戦略である純粋戦略を考え，そのナッシュ均衡が存在する条件について明らかにした．