# Prisoners' dilemma - Patrick McNutt

PRISONERS DILEMMA Co-operate or cheat: beyond individual choice In a game of imperfect information, players do not know game dimension, players are simply unaware of the actions chosen by other players. However if they know the other players type information is complete. In incomplete information games, players may or may not know some information about the other players - their type, their strategies, payoffs or their preferences but they have beliefs. Binary Preference Cooperate Reward No Reward Compete Punished

Not Punished Binary Preference Cooperate 1st preference ? Compete 4th preference ? PAYOFFS REFLECT PREFERENCE ORDER. GUARANTEED A 2 BUT THERE IS AN ELUSIVE 3 WHAT IF? STRATEGY I: COOPERATE

WHAT IF? STRATEGY II: COMPETE. THEN IF STRATEGY I IS THE CONSENSUS..? Strategy I Strategy II Strategy I 2,2 0,3 Strategy II 3,0 1,1 Nash Equilibrium WINNING IN TERMS OF NUMBER OF MOVES TRUST 8 Moves =

CHEAT 8 Moves = Move 1 = Rival Move 1 = Move 1 = Rival Move 1 = Move 2 = Rival Move 1 = Move 2 = Rival Move 2 = After 2 moves After 2 moves Move 3 = Rival Move 1 = Move 3 = Rival Move 3 = After 3 moves After 3 moves Move 4 = Rival Move 1 =

Move 4 = Rival Move 4 = Move 5 = Rival Move 1 = Move 5 = Rival Move 4 = Move 6 = Rival Move 1 = Move 6 = Rival Move 4 = Move 7 = Rival Move 1 = Move 7 = Rival Move 4 = Move 8 = Rival Move 1 = Move 8 = Rival Move 4 = THIEF OF NATURE Cheating on 2nd move after signalling trust on 1st move delivers 2 moves Short-term gain 2 moves > 2 moves

Indifference with thief of nature. Opponent likewise with I-think-You think-I-think and punishes the cheater for breaking trust. If knowledge of 8 moves then Shortterm gain < Long Term Benefit B (A,B) A Reciprocal Altruism Reciprocal Altruism 1st Preference Pro-active No Regrets Tough commitment & Trust Prisoners Dilemma ? Descartes Game Change

A lags behind, Costly Altruism for B unsustainable unilateral ? A Prisoners Dilemma 4th Preference Descartes Game Change B lags behind, Costly Altruism for A unsustainable unilateral Reactive Conflict All bets are off the table TRUST & COMMITMENT Co-operate

cheat Co-operate cheat 2,2 Kantian equilibrium 0,3 3,0 1,1 Nash equilibrium alliance No alliance alliance 2,2

Payoffdominant 0,1 No alliance 1,0 1,1 Play Games of Strategic Interaction The Prisoners Dilemma Conflict Trust & Commitment nflict & The Prisoners Dilemma Truhttp://ncase.me/trust/ http://www.patrickmcnutt.com/kaelo/kaelo.html

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