TY - JOUR

T1 - Alternating bid bargaining with a smallest money unit

AU - Van Damme, Eric

AU - Selten, Reinhard

AU - Winter, Eyal

PY - 1990/6

Y1 - 1990/6

N2 - In a seminal paper, Ariel Rubinstein has shown that impatience implies determinateness of the two-person bargaining problem. In this note we show that this result depends also on the assumption that the set of alternatives is a continuum. If the pie can be divided only in finitely many different ways (for example, because the pie is an amount of money and there is a smallest money unit), any partition can be obtained as the result of a subgame perfect equilibrium if the time interval between successive offers is sufficiently small. We also show that, for a fixed discount rate, all subgame perfect equilibrium payoffs of the discrete game converge to the solution obtained by Rubinstein if the smallest money unit tends to zero.

AB - In a seminal paper, Ariel Rubinstein has shown that impatience implies determinateness of the two-person bargaining problem. In this note we show that this result depends also on the assumption that the set of alternatives is a continuum. If the pie can be divided only in finitely many different ways (for example, because the pie is an amount of money and there is a smallest money unit), any partition can be obtained as the result of a subgame perfect equilibrium if the time interval between successive offers is sufficiently small. We also show that, for a fixed discount rate, all subgame perfect equilibrium payoffs of the discrete game converge to the solution obtained by Rubinstein if the smallest money unit tends to zero.

UR - http://www.scopus.com/inward/record.url?scp=0000974758&partnerID=8YFLogxK

U2 - 10.1016/0899-8256(90)90029-T

DO - 10.1016/0899-8256(90)90029-T

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AN - SCOPUS:0000974758

SN - 0899-8256

VL - 2

SP - 188

EP - 201

JO - Games and Economic Behavior

JF - Games and Economic Behavior

IS - 2

ER -