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Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the \"centipede game,\" however, players frequently violate this principle. An alternative is a \"dynamic level- k \" model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level- k rule is a best response to the level- (k-1) rule, and the level- ∞ rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Because the dynamic level- k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level- k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments. This paper was accepted by Peter Wakker, decision analysis.

We develop first-order smoothing techniques for saddle-point problems that arise in finding a Nash equilibrium of sequential games. The crux of our work is a construction of suitable prox-functions for a certain class of polytopes that encode the sequential nature of the game. We also introduce heuristics that significantly speed up the algorithm, and decomposed game representations that reduce the memory requirements, enabling the application of the techniques to drastically larger games. An implementation based on our smoothing techniques computes approximate Nash equilibria for games that are more than four orders of magnitude larger than what prior approaches can handle. Finally, we show near-linear further speedups from parallelization.

We study a cyber security game between a defender who wishes to defend her information assets and an attacker who tries to attack them. In this game the attacker and the defender choose how to distribute their resources in attacking or defending the different information assets. Given these investments the probability that an attack on a given asset is successful is an increasing function of the attacker’s investment and a decreasing function of the defender’s investment. The defender tries to minimize the expected damage from the attacks plus the cost of the defense while the attacker tries to maximize the expected damage from attacks minus his attacks’ expenses. The attacker is constrained by a budget. We compare two scenarios: a sequential move game and a simultaneous game. In the sequential game the defender moves first by deciding how much resources to allocate to the defense of each information asset and the attacker observes these investments and responds by allocating his resources in a manner that maximizes his expected utility. In the simultaneous game the attacker does not observe the defender’s decision before making his own. We analyze the best response strategies of the players and the equilibria of each of these games. Based on this analysis, we provide a tight upper bound on the reduction in defender’s costs that can be achieved by moving from the simultaneous to the sequential game.

Abstract-Assuming that the players with bounded rationality are randomly selected as the first movers or the second movers, and neither the first movers nor the second movers have dominant or weakly dominant strategies. This paper studied the group evolution dynamics based on symmetric sequential game with no dominant and weakly dominant strategies. First, it was found that there are no internal rest points in this type of evolutionary game, that is, one or some pure strategies must disappear with evolution, and every pure strategy has the possibility to eventually disappear. Then, the stability of these rest points was analyzed. The results show that when the sequential game has two PNE, there exist two symmetric PNE of the symmetric sequential game in the set of ESS, and there is at most one mixed strategy Nash equilibrium of symmetric sequential game. And when the sequential game has no PNE, there are no symmetric PNE of the symmetric sequential game in the set of ESS. Finally, numerical simulations were performed for the system dynamics when the sequential game path most favorable to the second movers is consistent or inconsistent with that most favorable to first movers in the case where the sequential game has two PNE, as well as for the system dynamics when the sequential game path most unfavorable to the second movers is consistent or inconsistent with that most favorable to the first movers in the absence case where the sequential game has no PNE.

In this paper, we apply game theory to identify equilibrium strategies for both attacker and defender in a fully endogenous model of resource allocation for countering terrorism and natural disasters. The key features of our model include balancing protection from terrorism and natural disasters, and describing the attacker choice by a continuous level of effort rather than a discrete choice (i.e., attack or not). Interestingly, in a sequential game, increased defensive investment can lead an attacker to either increase his level of effort (to help compensate for the reduced probability of damage from an attack), or decrease his level of effort (because attacking has become less profitable). This can either reduce or increase the effectiveness of investments in protection from intentional attack, and can therefore affect the relative desirability of investing in protection from natural disasters.

Firms have been increasing their information technology (IT) security budgets significantly to deal with increased security threats. An examination of current practices reveals that managers view security investment as any other and use traditional decision-theoretic risk management techniques to determine security investments. We argue in this paper that this method is incomplete because of the problem's strategic nature-hackers alter their hacking strategies in response to a firm's investment strategies. We propose game theory for determining IT security investment levels and compare game theory and decision theory approaches on several dimensions such as the investment levels, vulnerability, and payoff from investments. We show that the sequential game results in the maximum payoff to the firm, but requires that the firm move first before the hacker. Even if a simultaneous game is played, the firm enjoys a higher payoff than that in the decision theory approach, except when the firm's estimate of the hacker effort in the decision theory approach is sufficiently close to the actual hacker effort. We also show that if the firm learns from prior observations of hacker effort and uses these to estimate future hacker effort in the decision theory approach, then the gap between the results of decision theory and game theory approaches diminishes over time. The rate of convergence and the extent of loss the firm suffers before convergence depend on the learning model employed by the firm to estimate hacker effort.

Decision-making algorithms based on big data, artificial intelligence and other technologies are increasingly being applied to urban emergency decision-making, and urban smart emergency response is gradually appearing to be transformed from traditional empirical decision-making to human–machine collaborative decision-making. This paper explores the motivations for cooperative decision-making between leaders (human) and followers (machines) in urban emergency management in the presence of science and technology input spillovers. It focuses on the impact of human–machine cooperative decision-making on urban emergency response capacity, science and technology inputs and total urban emergency response benefits and discusses how to maximize the total benefits of urban emergency response under different levels of spillovers. In this paper, a three-stage dynamic game model is constructed: leaders and followers decide whether to establish a cooperative decision in the first stage; decide the level of science and technology inputs in the second stage; and compete for sequential decisions in the third stage. It was found that, firstly, unlike the case of static games, in sequential games, leaders and followers develop a willingness to cooperate in decision-making only when the spillover coefficients are in the lower range. Second, cooperative human–machine decision-making may diminish the importance of human experience in urban emergency management. Finally, the effectiveness of collaborative human–machine decision-making in urban emergencies deserves further research. The research in this paper provides recommendations for smart urban emergency management.

This study examines whether individuals can accurately predict trust and trustworthiness in others based on their appearance. Using photos and decisions from previous experimental trust games, subjects were asked to view the photos and guess the levels of trust and trustworthiness of the individuals depicted. The results show that subjects had little ability to accurately guess the trust and trustworthiness behavior of others. There is significant heterogeneity in the accuracy of guesses, and errors in guesses are systematically related to the observable characteristics of the photos. Subjects’ guesses appear to be influenced by stereotypes based on the features seen in the photos, such as gender, skin color, or attractiveness. These findings suggest that individuals’ beliefs that they can infer trust and trustworthiness from appearance are unfounded, and that efforts to reduce the impact of stereotypes on inferred trustworthiness may improve the efficiency of trust-based interactions.

Probabilistic selling (PS) is widely used in the travel industry and marketing practices; how to design a win-win contract using PS in multiple participants’ supply chain to achieve sustainable development has been a worthy concerned issue in the green supply chain development in China. To end this, we consider a three-players supply chain involving two firms and a common retailer in which the firms sell their transparent products via a dual channel, while the retailer sells probabilistic goods by a direct channel. First, the three players’ demand functions are derived using both a Hotelling model and taking account of consumers’ price reference effects. Second, we construct a probabilistic selling model for both decentralized and centralized supply chain systems. The optimal policies for the decentralized system are determined by employing Stackelberg sequential games and an analytical approach. Third, we propose a new three-way revenue sharing contract to deal with channel conflict. Furthermore, we determine the conditions under which the dual-channel supply chain can be coordinated to achieve a win–win situation for all participants. The results indicate that the retailer adopts probabilistic selling depending upon the relative values of the two manufacturers’ production costs in the three-way revenue sharing contract. More interestingly, PS not only can improve the supply chain’s efficiency, but also can coordinate the dual-channel supply chain to achieve a win-win situation for all participants. Finally, we present a numerical analysis to verify our results and a sensitivity analysis of the parameters involved.

This paper examines the tactical interaction between drones and tanks in modern warfare through game theory, particularly focusing on Stackelberg equilibrium and backward induction. It describes a high-stakes conflict between two teams: one using advanced drones for attack, and the other defending using tanks. The paper conceptualizes this as a sequential game, illustrating the complex strategic dynamics similar to Stackelberg competition, where moves and countermoves are carefully analyzed and predicted.