An Experimental Analysis of Asymmetric Power in Conflict Bargaining

Abstract

Demands and concessions in a multi-stage bargaining process are shaped by the probabilities that each side will prevail in an impasse. Standard game-theoretic predictions are quite sharp: demands are pushed to the precipice with nothing left on the table, but there is no conflict regardless of the degree of power asymmetry. Indeed, there is no delay in reaching an agreement that incorporates the (unrealized) costs of delay and conflict. A laboratory experiment has been used to investigate the effects of power asymmetries on conflict rates in a two-stage bargaining game that is (if necessary) followed by conflict with a random outcome. Observed demands at each stage are significantly correlated with power, as measured by the probability of winning in the event of disagreement. Demand patterns, however, are flatter than theoretical predictions, and conflict occurs in a significant proportion of the interactions, regardless of the degree of the power asymmetry. To address these deviations from the standard game-theoretic predictions, we also estimated a logit quantal response model, which generated the qualitative patterns that are observed in the data. This one-parameter generalization of the Nash equilibrium permits a OPEN ACCESSGames 2013, 4 376 deconstruction of the strategic incentives that cause demands to be less responsive to power asymmetries than Nash predictions.Keywords: bargaining; conflict; quantal response equilibrium; laboratory experiments 1 See Holt and Roth [10] for specific references and a perspective on motivations for early work on game theory and on the Nash equilibrium in particular. The finite-stage bargaining models considered in this paper can be solved by backward induction, using Reinhard Selten's notion of subgame perfection to rule out Nash equilibria that involve non-credible threats to reject favorable offers. 2 Numerous variants of the bargaining model arise in the political science literature. We focus on a two-stage version of the model analyzed in Fearon [5].

Bargaining in the shadow of a commitment problem

“…Though subjects sharply distinguish between games with and without commitment problem conditions, their bargaining demands are substantially less sharp, diverging from Nash in ways consistent with other laboratory analyses of bargaining protocols (Sieberg et al, 2013). Moreover, subject demands are statistically indistinguishable between the two-stage and ultimatum games.…”

“…In recent work, other scholars use experiments to examine rationalist claims in bargaining protocols (Quek, forthcoming; Sieberg et al, 2013) and to examine bargaining choices given expectations regarding future interactions (Kertzer and Rathbun, 2015; Tingley, 2011). The specific commitment problem we examine in this paper unfolds in a bargaining context where two parties disagree over the division of some good.…”

Stochastic game theory for social science: a primer on quantal response equilibrium

“…The resulting equilibrium statistical models can be used to incorporate insights and biases that are documented in research on behavioral economics, for example, the effects of inequity aversion, regret, altruism or risk aversion in auctions and games. 22 Quantal response equilibrium has also been applied to sequential games (for example, McKelvey and Palfrey 1992Palfrey , 1998Sieberg et al 2013), where quantal continuation values are used to calculate equilibria that exhibit a generalized version of subgame perfection. These quantal continuation values make it possible to look 'inside the box' and gain an understanding of the underlying process that generates intuitive but systematic departures from theoretical predictions, departures that arise naturally from intersections or interactions of smoothed quantal responses that replace sharp corners implicit in standard models with perfect rationality.…”

Balance of power and the propensity of conflict

“…They …nd that players are less sensitive to changes in their bargaining position than theory predicts, as the players closely stick to the 50-50 split. Sieberg et al (2013) study the e¤ect of power asymmetries in a two-stage alternating o¤er game with shrinking pie; if no agreement is reached, a lottery with exogenous win probabilities determines the allocation. They …nd no clear relationship between the probability of early agreement and power asymmetry.…”