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Two players divide a cake SEach in his turn makes an offer, which the other accepts or rejects. The game ends when someone acceptsThe players alternate in making offersThere is a discount rate of Sequential Bargaining(Rubinstein Bargaining Model)
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Sequential Bargaining(Rubinstein Bargaining Model)1(x,y) S(x,y)denote these stages by 1/2i.e. 1 makes an offer,2 accepts or rejects 2YN(x, y)21(x,y) St = 1etc.
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Strategies234
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Strategies2t = 1t = 2t = 3
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Sequential Bargaining(Rubinstein Bargaining Model)1/2payoffs2t = 1t = 2t = 3
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Nash Equilibria234
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria234
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria234
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria234
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaCan be supported as an equilibrium payoffCan be supported as an equilibrium payoff?
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibriausing similar arguments
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaCheck that it is a SPE !!
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaGraphically
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaShow that there is a unique SPE, and that its payoff is:
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Optiona+b < 1
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option1/211
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Optionb(1+b)/2(1-b)/2
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside OptionNash Bargaining Solution
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Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside OptionNash Bargaining Solution The Nash Bargaining solution increases with b The Outside Option equilibrium remains constant for small b
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiationsafter an offer is rejected, Nature breaks down the negotiations with probability p negotiations continue with probability 1-pNo need to have a discount rate !!
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiations
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiations
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiationsThe payoff of player 2 :
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiations
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Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiationsEND
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