Chapter 28 Game Theory
Chapter 28 Game Theory
Three fundamental elements to describe a game: oPlayers, o(pure)strategies or actions, opayoffs
Three fundamental elements to describe a game: ⚫Players, ⚫(pure) strategies or actions, ⚫payoffs
Color Matching B b 1,-1 -1, A r -1,1 1,-1
B b r b A r 1, -1 -1, 1 -1, 1 1, -1 Color Matching
Payoff matrices for Two-person games. Simultaneous(-move) games. Finite games:Both the numbers of players and of alternative pure strategies are finite
Payoff matrices for Two-person games. Simultaneous(-move) games. Finite games: Both the numbers of players and of alternative pure strategies are finite
The Prisoner's Dilemma B Confess Deny Confess -3*,-3* A Deny 5,0
B Confess Deny Confess A Deny -3* , -3* 0, -5 -5, 0 -1, -1 The Prisoner’s Dilemma
o Dominant strategies,and dominated strategies. Method of iterated elimination of strictly dominated strategies
⚫ Dominant strategies, and dominated strategies. ⚫ Method of iterated elimination of strictly dominated strategies
OThe Prisoner's Dilemma shows also that a Nash equilibrium does not necessarily lead to a Pareto efficient outcome. ●Two-win games
⚫The Prisoner’s Dilemma shows also that a Nash equilibrium does not necessarily lead to a Pareto efficient outcome. ⚫Two-win games
OA pair of strategies is a Nash equilibrium if A's choice is optimal given B's choice, and vice versa. oNash is a situation, or a strategy combination of no incentive to deviate unilaterally
⚫A pair of strategies is a Nash equilibrium if A’s choice is optimal given B’s choice, and vice versa. ⚫Nash is a situation, or a strategy combination of no incentive to deviate unilaterally
Battle of Sexes Girl Soccer Ballet Soccer 2*,1* 0, Boy Ballet -1,-1 1*,2*
Girl Soccer Ballet Soccer Boy Ballet 2* , 1* 0, 0 -1, -1 1* , 2* Battle of Sexes
oMethod of underlining relatively advantageous strategies. oDouble underlining gives Nash. oThere can be no,one,and multiple (pure)Nash equilibria
⚫Method of underlining relatively advantageous strategies. ⚫Double underlining gives Nash. ⚫There can be no, one, and multiple (pure) Nash equilibria