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Introduction to game theory and negotiation

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    1. Introduction to game theory and negotiation Ville Koskinen Raimo P Hmlinen Systems Analysis Laboratory Helsinki University of Technology

    2. Contents Prisoners dilemma and the problem of the commons: Basic concepts in game theory Negotiation analysis Aid for co-operation Example of the methods in negotiation analysis: Jointly improving direction method

    3. Prisoners dilemma Two friends, Harold and William, are suspected of committing a crime They are separated They are unable to communicate and act co-operatively They may take two actions: to confess or not to confess the crime

    4. Consequences Neither of them confesses Both of them will be convicted of a minor offence and sentenced to 1 month in jail Both of them confess They will be sentenced to jail for 6 months Only one of them confesses The confessor acts as a witness against the other The confessor will be freed The other will be sentenced to 9 months in jail

    5. Representation as a game Players: Harold and William Strategy for each player, to confess (c) or not to confess (nc): s1?S1={c,nc} and s2?S2= {c,nc} 1 refers to Harold and 2 refers to William The payoff for each player: Number of months in prison + negative sign, denoted by ui(s1,s2), i?{1,2}

    6. Best response strategies Williams best response strategy is c, if Harold chooses nc c, if Harold chooses c Likewise, Harolds best response is c independently of Williams choice