GAME THEORY AND APPLICATIONS INTRODUCTION Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli History Antoine Cournot (1838): duopoly application John von Neuman (1928): theory of parlor games John von Neuman and Oskar Morgenstern (1944) : Theory of Games and Economic Behaviour John Nash (1950): Nash Equilibirum Nash, Harsanyi, Selten (1994): Nobel Prize Aumann and Schelling (2005): Nobel Prize Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli A game is a formal description of strategic situation. Game theory is the formal study of decision-making where several players must make choices that potentially affect the interest of other players. Cooperative game theory investigates coalitional games with respect to the amounts of power held by various players or how a successful coalition should divide its proceeds. Noncooperative game theory investigates the analysis of strategic choices. The ordering and the timing of players’ choices are crucial to the outcome of the game. Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Strategic form (normal form): Each player’s strategies and outcomes resulting from each possible combination of choices are listed. An outcome is presented by a seperate pay-off for each player that measures how much the player likes the outcome or how much the player will obtain by playing that strategy. Extensive form (game tree): Complete description of how the game is played over time, including order, information of players, payoffs, probabilities. Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Nash equilibrium Nash Equilibrium is a list of strategies, one for each player, which has the property that no player can unilaterally change that strategy and get a better payoff. Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Some Important Games Zero-sum Games Positive sum Games Games without Equilibrium Games with Multiple Equilibria Prisoner’s Dilemma Battle of the Sexes Chicken or Hawk versus Dove Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Player2 Player1 heads tails (1,-1) (-1, 1) (1, -1) Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Player2 Player1 football opera (3,2) (1, 1) (2,3) Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Player2 Player1 tough chicken (-4,-4) (10,-1) (-1, 10) (5,5) Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Player2 Player1 cooperate defect (-1,-1) (-8, 0) (0, -8) (-3,-3) Assoc. Prof. Yeşim Kuştepeli

Assoc. Prof. Yeşim Kuştepeli Other terminology Symmetric Games Repeated Games Nonrepeated Games Maxi-min strategy Pure strategy Mixed strategy Static vs. Dynamic Games Assoc. Prof. Yeşim Kuştepeli