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)

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.

Sequential Bargaining(Rubinstein Bargaining Model)1/2Strategies234

Sequential Bargaining(Rubinstein Bargaining Model)1/2Strategies2t = 1t = 2t = 3

Sequential Bargaining(Rubinstein Bargaining Model)1/2payoffs2t = 1t = 2t = 3

Sequential Bargaining(Rubinstein Bargaining Model)1/2Nash Equilibria234

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria234

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria234

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria234

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaCan be supported as an equilibrium payoffCan be supported as an equilibrium payoff?

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibriausing similar arguments

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect Equilibria

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaCheck that it is a SPE !!

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaGraphically

Sequential Bargaining(Rubinstein Bargaining Model)1/2Subgame Perfect EquilibriaShow that there is a unique SPE, and that its payoff is:

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Optiona+b < 1

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Option1/211

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside Optionb(1+b)/2(1-b)/2

Sequential Bargaining(Rubinstein Bargaining Model)1/223Bargaining with an Outside OptionNash Bargaining Solution

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

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 !!

Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiations

Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiations

Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiationsThe payoff of player 2 :

Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiations

Sequential Bargaining(Rubinstein Bargaining Model)1/2Bargaining with random breakdown of negotiationsEND

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