Download Bargaining and Markets (Economic Theory, Econometrics, and by Martin J. Osborne PDF

By Martin J. Osborne

The formal concept of bargaining originated with John Nash's paintings within the early Fifties. This publication discusses fresh advancements during this conception. the 1st makes use of the software of intensive video games to build theories of bargaining within which time is modeled explicitly. the second one applies the speculation of bargaining to the examine of decentralized markets. instead of surveying the sector, the authors current a pick out variety of versions, every one of which illustrates a key element. additionally, they provide special proofs in the course of the publication. It makes use of a small variety of types, instead of a survey of the sphere, to demonstrate key issues, and comprises precise proofs given as motives for the types. The textual content has been class-tested in a semester-long graduate path.

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Extra resources for Bargaining and Markets (Economic Theory, Econometrics, and Mathematical Economics)

Example text

3 Comparative statics of the Nash solution for the problem of dividing a dollar. If the utility functions of the players are ui (i = 1,2) then Player 1 receives zu units of the dollar in the Nash solution. If Player 2 has the utility function v2 = h ◦ u2 , where h is increasing and concave (so that Player 2 is more risk-averse), while Player 1 retains the utility function u1 , then Player 1 receives zv in the Nash solution.

In the case of bargaining over the division of a dollar, we interpret xi as the amount that Player i receives. In the case of negotiating the sale price of an indivisible good, x1 is the price the buyer pays to the seller. In the model of wage negotiation, x1 is the profit of the firm. The bargaining procedure is as follows. The players can take actions only at times in the (infinite) set T = {0, 1, 2, . }. In each period t ∈ T one of the players, say i, proposes an agreement (a member of X), and the other player (j) either accepts the offer (chooses Y ) or rejects it (chooses N ).

The optimality of actions proposed at unreached nodes is not tested when we ask if a strategy pair is a Nash equilibrium. If the two strategies τ and τ of Player 2 differ only in the actions they prescribe at nodes that are not reached when Player 1 uses the strategy σ, then (σ, τ ) and (σ, τ ) yield the same path through the tree; hence Player 2 is indifferent between τ and τ when Player 1 uses σ. To be specific, consider the strategy τ of Player 2 that differs from the strategy τ defined in the previous section only in period 0, when Player 2 accepts some offers x in which x2 < x2 .

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