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

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\u27s 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\u27 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\u27 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

Analyzing Policy Risk and Accounting for Strategy: Auctions in the National Airspace System

We examine the potential for simple auction mechanisms to efficiently allocate arrival and departure slots during Ground Delay Programs (GDPs). The analysis is conducted using a new approach to predicting strategic behavior called Predictive Game Theory (PGT). The difference between PGT and the familiar Equilibrium Concept Approach (ECA) is that PGT models produce distribution-valued solut tion concepts rather than set-valued ones. The advantages of PGT over ECA in policy analysis and design are that PGT allows for decision-theoretic prediction and policy evaluation. Furthermore, PGT allows for a comprehensive account of risk, including two types of risk, systematic and modeling, that cannot be considered with the ECA. The results show that the second price auction dominates the first price auction in many decision-relevant categories, including higher expected efficiency, lower variance in efficiency, lower probability of significant efficiency loss and higher probability of significant efficiency gain. These findings are despite the fact that there is no a priori reason to expect the second price auction to be more efficient because none of the conventional reasons for preferring second price over first price auctions, i.e. dominant strategy implementability, apply to the GDP slot auction setting.auction, ground delay program, entropy, predictive game theory, strategic risk

Learning with bounded memory.

The paper studies infinite repetition of finite strategic form games. Players use a learning behavior and face bounds on their cognitive capacities. We show that for any given beliefprobability over the set of possible outcomes where players have no experience. games can be payoff classified and there always exists a stationary state in the space of action profiles. In particular, if the belief-probability assumes all possible outcomes without experience to be equally likely, in one class of Prisoners' Dilemmas where the average defecting payoff is higher than the cooperative payoff and the average cooperative payoff is lower than the defecting payoff, play converges in the long run to the static Nash equilibrium while in the other class of Prisoners' Dilemmas where the reserve holds, play converges to cooperation. Results are applied to a large class of 2 x 2 games.Cognitive complexity; Bounded logistic quantal response learning; Long run outcomes;

Human-Agent Decision-making: Combining Theory and Practice

Extensive work has been conducted both in game theory and logic to model strategic interaction. An important question is whether we can use these theories to design agents for interacting with people? On the one hand, they provide a formal design specification for agent strategies. On the other hand, people do not necessarily adhere to playing in accordance with these strategies, and their behavior is affected by a multitude of social and psychological factors. In this paper we will consider the question of whether strategies implied by theories of strategic behavior can be used by automated agents that interact proficiently with people. We will focus on automated agents that we built that need to interact with people in two negotiation settings: bargaining and deliberation. For bargaining we will study game-theory based equilibrium agents and for argumentation we will discuss logic-based argumentation theory. We will also consider security games and persuasion games and will discuss the benefits of using equilibrium based agents.Comment: In Proceedings TARK 2015, arXiv:1606.0729

Modeling customer bounded rationality in operations management: A review and research opportunities

Many studies in operations management started to explicitly model customer behavior. However, it is typically assumed that customers are fully rational decision-makers and maximize their utility perfectly. Recently, modeling customer bounded rationality has been gaining increasing attention and interest. This paper summarizes various approaches of modeling customer bounded rationality, surveys how they are applied to relevant operations management settings, and presents the new insights obtained. We also suggest future research opportunities in this important area

Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making

While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we focus on some of the assumptions underlying rationality such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-$k$ reasoning and quantal response equilibrium (QRE) respectively. Specifically, we provide an information-theoretic two-parameter model that can relax both mutual consistency and best response, but can recover approximations of level-$k$, QRE, or typical Nash equilibrium behaviour in the limiting cases. The proposed Quantal Hierarchy model is based on a recursive form of the variational free energy principle, representing self-referential games as (pseudo) sequential decisions. Bounds in player processing abilities are captured as information costs, where future chains of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the applicability of the proposed model to several canonical economic games.Comment: 36 pages, 15 figure

A cognitive hierarchy theory of one-shot games: Some preliminary results

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modelling principles in noncooperative game theory. This paper relaxes mutual consistency to predict how players are likely to behave in in one-shot games before they can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f (k). Zero-step players randomize. Players using k (≥ 1) steps best respond given partially rational expectations about what players doing 0 through k - 1 steps actually choose. A simple axiom which expresses the intuition that steps of thinking are increasingly constrained by working memory, implies that f (k) has a Poisson distribution (characterized by a mean number of thinking steps τ ). The CH model converges to dominance-solvable equilibria when τ is large, predicts monotonic entry in binary entry games for τ < 1:25, and predicts effects of group size which are not predicted by Nash equilibrium. Best-fitting values of τ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable p-beauty contests. The CH model also has economic value because subjects would have raised their earnings substantially if they had best-responded to model forecasts instead of making the choices they did

The influence of topology and information diffusion on networked game dynamics

This thesis studies the influence of topology and information diffusion on the strategic interactions of agents in a population. It shows that there exists a reciprocal relationship between the topology, information diffusion and the strategic interactions of a population of players. In order to evaluate the influence of topology and information flow on networked game dynamics, strategic games are simulated on populations of players where the players are distributed in a non-homogeneous spatial arrangement. The initial component of this research consists of a study of evolution of the coordination of strategic players, where the topology or the structure of the population is shown to be critical in defining the coordination among the players. Next, the effect of network topology on the evolutionary stability of strategies is studied in detail. Based on the results obtained, it is shown that network topology plays a key role in determining the evolutionary stability of a particular strategy in a population of players. Then, the effect of network topology on the optimum placement of strategies is studied. Using genetic optimisation, it is shown that the placement of strategies in a spatially distributed population of players is crucial in maximising the collective payoff of the population. Exploring further the effect of network topology and information diffusion on networked games, the non-optimal or bounded rationality of players is modelled using topological and directed information flow of the network. Based on the topologically distributed bounded rationality model, it is shown that the scale-free and small-world networks emerge in randomly connected populations of sub-optimal players. Thus, the topological and information theoretic interpretations of bounded rationality suggest the topology, information diffusion and the strategic interactions of socio-economical structures are cyclically interdependent

The influence of topology and information diffusion on networked game dynamics

This thesis studies the influence of topology and information diffusion on the strategic interactions of agents in a population. It shows that there exists a reciprocal relationship between the topology, information diffusion and the strategic interactions of a population of players. In order to evaluate the influence of topology and information flow on networked game dynamics, strategic games are simulated on populations of players where the players are distributed in a non-homogeneous spatial arrangement. The initial component of this research consists of a study of evolution of the coordination of strategic players, where the topology or the structure of the population is shown to be critical in defining the coordination among the players. Next, the effect of network topology on the evolutionary stability of strategies is studied in detail. Based on the results obtained, it is shown that network topology plays a key role in determining the evolutionary stability of a particular strategy in a population of players. Then, the effect of network topology on the optimum placement of strategies is studied. Using genetic optimisation, it is shown that the placement of strategies in a spatially distributed population of players is crucial in maximising the collective payoff of the population. Exploring further the effect of network topology and information diffusion on networked games, the non-optimal or bounded rationality of players is modelled using topological and directed information flow of the network. Based on the topologically distributed bounded rationality model, it is shown that the scale-free and small-world networks emerge in randomly connected populations of sub-optimal players. Thus, the topological and information theoretic interpretations of bounded rationality suggest the topology, information diffusion and the strategic interactions of socio-economical structures are cyclically interdependent