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Stackelberg competition
About: Stackelberg competition is a research topic. Over the lifetime, 6611 publications have been published within this topic receiving 109213 citations.
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Proceedings Article•
22 Jul 2012
TL;DR: TRUSTS as discussed by the authors models the problem of computing patrol strategies as a leader-follower Stackelberg game, where the objective is to deter fare evasion and hence maximize revenue.
Abstract: In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of such fines depends on the unpredictability and effectiveness of the patrols. In this paper, we present TRUSTS, an application for scheduling randomized patrols for fare inspection in transit systems. TRUSTS models the problem of computing patrol strategies as a leader-follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism-motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge. A third key novelty in our work is deliberate simplification of leader strategies to make patrols easier to be executed. We present an efficient algorithm for computing such patrol strategies and present experimental results using real-world ridership data from the Los Angeles Metro Rail system. The Los Angeles County Sheriff's department has begun trials of TRUSTS.
94 citations
06 May 2013
TL;DR: This work presents a general Bayesian Stackelberg game model for security patrolling in dynamic uncertain domains, in which the uncertainty in the execution of patrols is represented using Markov Decision Processes and shows that patrol schedules generated using this approach outperform schedules generated with a previous algorithm that does not consider execution uncertainty.
Abstract: In recent years there has been extensive research on game-theoretic models for infrastructure security. In time-critical domains where the security agency needs to execute complex patrols, execution uncertainty(interruptions) affect the patroller's ability to carry out their planned schedules later. Indeed, experiments in this paper show that in some real-world domains, small fractions of execution uncertainty can have a dramatic impact. The contributions of this paper are threefold. First, we present a general Bayesian Stackelberg game model for security patrolling in dynamic uncertain domains, in which the uncertainty in the execution of patrols is represented using Markov Decision Processes. Second, we study the problem of computing Stackelberg equilibrium for this game. We show that when the utility functions have a certain separable structure, the defender's strategy space can be compactly represented, and we can reduce the problem to a polynomial-sized optimization problem. Finally, we apply our approach to fare inspection in the Los Angeles Metro Rail system. Numerical experiments show that patrol schedules generated using our approach outperform schedules generated using a previous algorithm that does not consider execution uncertainty.
94 citations
01 Jan 1992
TL;DR: In this article, a game of CO2 emissions is considered in the context of international environmental agreement as games, where the goal is to find the optimal solution to a set of environmental problems.
Abstract: Editor's Introduction.- Editor's Introduction.- 1: International Dimensions.- 1 International Environmental Agreements as Games.- 1. Introduction.- 2. Reaching agreement.- 2.1. Identical countries.- 2.2. Cost differences.- 2.3. Benefit differences.- 2.4. Choice of a benchmark.- 2.5. Summary.- 3. Sustaining agreement.- References.- Comments by Henk Folmer.- 2 Emission Taxes in a Dynamic International Game of CO2 Emissions.- 1. Introduction.- 2. A static game.- 3. A dynamic game.- 4. The open loop equilibrium without taxes.- 5. The Markov perfect equilibrium without taxes.- 6. Other subgame perfect equilibria.- 7. Pigouvian taxes.- 8. Non-commitment and taxation.- References.- Comments by Otto Keck.- 3 Critical Loads and International Environmental Cooperation.- 1. Critical loads.- 2. Naive interpretations.- 3. Stock of pollutants - the case of one country.- 4. Stock of pollutants - several countries and the open loop equilibrium.- 5. Closed loop or feed back equilibria.- References.- Comments by Henry Tulkens.- 4 Environmental Conflicts and Strategic Commitment.- 1. Introduction.- 2. Analytical framework.- 3. Asymmetric players and endogenous strategic timing.- 4. N players and strategic team formation.- 5. Conclusion.- References.- Comments by Detlev Homann.- 5 The Choice of Environmental Policy Instruments and Strategic International Trade.- 1. Introduction.- 2. The model.- 3. Single stage Cournot model.- 4. Two stage Stackelberg model.- 5. Two stage Cournot model.- 6. Conclusions.- References.- Comments by Marji Lines.- 6 Economic Models of Optimal Energy Use under Global Environmental Constraints.- 1: The CO2 Problem in Basic Models of Optimal Use of Fossil Fuels.- 2. Background problem on climatic change and global environmental constraints.- 3. Economic studies on the CO2 problem.- 4. Preliminary definitions and the general model.- 5. A simplified model.- 5.1. Necessary conditions.- 5.2. Sufficient conditions.- 5.3. Definition and optimality of equilibrium.- 5.4. Illustration by a phase plane diagram.- 6. A discrete type impact of CO2 emissions.- 7. Further specification of the model.- 8. Discussion.- 2: Technical Change, International Co-operation, and Structural Uncertainty.- 10. A taxonomy of technical change.- 11. Neutral technical change in a general model.- 12. International co-operation.- 13. Structural uncertainty.- 13.1. Modelling uncertainty about critical CO2 levels as uncertainty about a critical, limited natural resource.- 13.2. Treating structural uncertainty.- 13.3. Numerical calculations.- 14. Conclusions and perspectives.- Appendix A: Existence and Uniqueness of the Optimal Solution.- Appendix B: Existence and Stability of Equilibrium.- References.- Comments by Oskar Von Dem Hagen.- Comments by Cees Withagen.- 2: Monitoring and Enforcement.- 7 Monitoring and Enforcement of Pollution Control Laws in Europe and the United States.- 1. Introduction.- 2. Differences among monitoring and enforcement problems and systems.- 3. Key dimensions of monitoring and enforcement systems.- 3.1. Probability of monitoring.- 3.2. Surprise.- 3.3. Definition of a violation.- 3.4. Penalties and other responses to violations.- 4. Some evidence on European & U.S. choices in monitoring & enforcement.- 5. A glimpse of the future? Recommendations from the U.K. (The "Kinnersley Report").- 6. Concluding comments.- References.- Comments by Heinz Welsch.- 8 The Economics of Negotiations on Water Quality - An Application of Principal Agent Theory.- 1. Introduction.- 2. The basic model structure of a modified LEN-model.- 3. The basic model with a beta-distribution of water quality depending on abatement intensity.- 4. Possible extensions.- References.- Comments by Gunther knieps.- 9 Monitoring the Emission of Pollutants by Means of the Inspector Leadership Method.- 1. Monitoring point sources of pollution.- 2. Decision theoretical formulation of the problem.- 3. Comparison of the solutions of the simple' simultaneous' and 'leadership' games.- 4. The general inspector leadership game and the Neyman -Pearson lemma.- 5. Application.- 6. Concluding remarks.- References.- Comments by Till Requate.- 10 Illegal Pollution and Monitoring of Unknown Quality - A Signaling Game Approach -.- 1. Introduction.- 1: Equilibrium Scenarios with Pooling and Signaling Behavior.- 2. The game model.- 3. A gallery of equilibrium scenarios.- 3.1. Pooled shirking and illegal waste disposal: 'polluter's paradise scenario'.- 3.2. Exploratory accidents and illegal waste disposal due to unqualified control: 'signaling scenarios'.- 3.3. Absence of illegal pollution due to efficient control: 'controller's paradise scenario'.- 3.4. Intermediate illegal pollution: 'constrained polluter's paradise scenario'.- 3.5. Equilibrium scenarios and the multiplicity of equilibria.- 2: Perfect Equilibria and (Unique) Solutions via Equilibrium Selection.- 4. Uniformly perfect pure strategy equilibria.- 5. Comparison of signaling and pooling equilibria.- 5.1. Cell and truncation consistency.- 5.2. Payoff dominance.- 5.3. Risk dominance.- 5.4. Solutions in the range (4.14).- 5.5. The solution in the range (4.15).- 5.6. Discussion of the solution.- 6. Conclusions.- References.- Comments by Aart de Zeeuw.
94 citations
TL;DR: In this article, the authors study a supply chain comprising two competing manufacturers who sell their products through a common retailer, where the retailer sells two competing brands with varying degrees of product substitutability, under a linear stochastic demand, which is dependent on the retailer's price of its own brand as well as on the competing brand's retail price.
93 citations
TL;DR: A game theoretic resource allocation scheme for media cloud to allocate resource to mobile social users though brokers and results show that each player in the game can obtain the optimal strategy where the Stackelberg equilibrium exists stably.
Abstract: Due to the rapid increases in both the population of mobile social users and the demand for quality of experience (QoE), providing mobile social users with satisfied multimedia services has become an important issue. Media cloud has been shown to be an efficient solution to resolve the above issue, by allowing mobile social users to connect to it through a group of distributed brokers. However, as the resource in media cloud is limited, how to allocate resource among media cloud, brokers, and mobile social users becomes a new challenge. Therefore, in this paper, we propose a game theoretic resource allocation scheme for media cloud to allocate resource to mobile social users though brokers. First, a framework of resource allocation among media cloud, brokers, and mobile social users is presented. Media cloud can dynamically determine the price of the resource and allocate its resource to brokers. A mobile social user can select his broker to connect to the media cloud by adjusting the strategy to achieve the maximum revenue, based on the social features in the community. Next, we formulate the interactions among media cloud, brokers, and mobile social users by a four-stage Stackelberg game. In addition, through the backward induction method, we propose an iterative algorithm to implement the proposed scheme and obtain the Stackelberg equilibrium. Finally, simulation results show that each player in the game can obtain the optimal strategy where the Stackelberg equilibrium exists stably.
93 citations