Modeling Bounded Rationality in Capacity Allocation Games with the Quantal Response Equilibrium

Abstract

We consider a supply chain with a single supplier and two retailers. The retailers choose their orders strategically, and if their orders exceed the supplier's capacity, quantities are allocated proportionally to the orders. We experimentally study the capacity allocation game using subjects motivated by financial incentives. We find that the Nash equilibrium, which assumes that players are perfectly rational, substantially exaggerates retailers' tendency to strategically order more than they need. We propose a model of bounded rationality based on the quantal response equilibrium, in which players are not perfect optimizers and they face uncertainty in their opponents' actions. We structurally estimate model parameters using the maximumlikelihood method. Our results confirm that retailers exhibit bounded rationality, become more rational through repeated game play, but may not converge to perfect rationality as assumed by the Nash equilibrium. Finally, we consider several alternative behavioral theories and show that they do not explain our experimental data as well as our bounded rationality model. Abstract:We consider a supply chain with a single supplier and two retailers. The retailers choose their orders strategically and if their orders exceed the supplier's capacity, quantities are allocated proportionally to the orders. We experimentally study the capacity allocation game using subjects motivated by financial incentives. We find that the Nash Equilibrium, which assumes that players are perfectly rational, substantially exaggerates retailers' tendency to strategically order more than they need.We propose a model of bounded rationality based on the Quantal Response Equilibrium, in which players are not perfect optimizers and they face uncertainty in their opponents' actions. We structurally estimate model parameters using the maximum likelihood method. Our results confirm that retailers exhibit bounded rationality, become more rational through repeated game play, but may not converge to perfect rationality as assumed by the Nash equilibrium. Finally, we consider several alternative behavioral theories and show that they do not explain our experimental data as well as our bounded rationality model.

Information Reliability in Supply Chains: The Case of Multiple Retailers

“…(2012) [13]. They consider a setting of complete information, capacity shortage, known demands and proportional allocation.…”

“…This case allows us to study trustworthiness and trusting behavior in demand forecast sharing in a very simple setting with multiple retailers and privately known deterministic demands. Recent research shows that when demand is deterministic and capacity is binding, Nash equilibrium predictions substantially exaggerate retailers' tendency to strategically order more than they need in order to gain a more favorable allocation [13].…”

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

“…Our work is also closely related to the research on the decision-making mechanism of bounded rational players [27][28][29]. Among this stream of literature, these studies that investigate the dynamic adjustment of players with limited information in competitive settings are most close to our study.…”

For the sustainable performance of the carbon reduction labeling policies under an evolutionary game simulation

“…One key assumption is that players are perfectly rational and have common knowledge of this rationality (Samuelson, 2002). This assumption indicates that players who strive to maximize their utilities are capable of thinking through all the possible solutions and choosing the appropriate course of action (Chen et al, 2012). However, Shubik (2002) and Szabó and Fath (2007) pointed out that such an assumption was inconsistent with the real world because individual rationality was restricted by the available information, cognitive limitations, and time available to make decisions.…”