Cognition and framing in sequential bargaining for gains and losses

Abstract

Noncooperative game-theoretic models of sequential bargaining give an \nunderpinning to cooperative solution concepts derived from axioms, and \nhave proved useful in applications (see Osborne and Rubinstein 1990). But \nexperimental studies of sequential bargaining with discounting have generally \nfound systematic deviations between the offers people make and perfect \nequilibrium offers derived from backward induction (e.g., Ochs and \nRoth 1989). \nWe have extended this experimental literature in two ways. First, \nwe used a novel software system to record the information subjects \nlooked at while they bargained. Measuring patterns of information search \nhelped us draw inferences about how people think, testing as directly \nas possible whether people use backward induction to compute offers. \nSecond, we compared bargaining over gains that shrink over time (because \nof discounting) to equivalent bargaining over losses that expand over \ntime. \nIn the games we studied, two players bargain by making a finite number \nof alternating offers. A unique subgame-perfect equilibrium can be computed \nby backward induction. The induction begins in the last period and \nworks forward. Our experiments use a three-round game with a pie of \n$5.00 and a 50-percent discount factor (so the pie shrinks to $2.50 and \n$1.25 in the second and third rounds). In the perfect equilibrium the first \nplayer offers the second player $1.25 and keeps $3.75.

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