Extensive Form Games Research Articles

Insider trading in discrete time Kyle games

AbstractWe present a new discrete time version of Kyle’s (Econometrica 53(6):1315–1335, 1985) classic model of insider trading, formulated as a generalised extensive form game. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise expected profits while the market maker observes the total order flow and sets prices accordingly. First, we show how the multi-period model with finitely many pure strategies can be reduced to a (static) social system in the sense of Debreu (Proc Natl Acad Sci 38(10):886–893, 1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (Econometrica 50(4):863–894, 1982). This works for any probability distribution with finite support of the noise trader’s demand and the true value, and for any finite information flow of the insider. In contrast to Kyle (1985) with normal distributions, equilibria exist in general only in mixed strategies and not in pure strategies. In the single-period model we establish bounds for the insider’s strategy in equilibrium. Finally, we prove the existence of an equilibrium for the game with a continuum of actions, by considering an approximating sequence of games with finitely many actions. Because of the lack of compactness of the set of measurable price functions, standard infinite-dimensional fixed point theorems are not applicable.

Theoretical properties of the MiCRO negotiation strategy

Recently, we have introduced a new algorithm for automated negotiation, called MiCRO, which, despite its simplicity, outperforms many state-of-the-art negotiation strategies (de Jonge, in: Raedt (ed) Proceedings of the thirty-first international joint conference on artificial intelligence, ijcai.org, Vienna, Austria, 2022). Furthermore, we claimed that under certain conditions which typically hold in the Automated Negotiating Agents Competition (ANAC), it is a game-theoretically optimal strategy. The goal of this paper is to formally prove those claims. Specifically, we define ‘negotiation’ as an extensive-form game and define the class of consistent strategies for this game, which consists of those strategies that satisfy a number of rationality criteria. We then prove that under the above mentioned conditions MiCRO is a best response against itself among all consistent negotiation strategies. Furthermore, we define the notion of a balanced negotiation domain, which is a domain in which two MiCRO agents would always come to an optimal agreement. Finally, we show that many of the domains used in ANAC indeed happen to be (approximately) balanced. The importance of this work is that if we know under which conditions MiCRO is theoretically optimal, then we can use this to test to what extent other negotiation algorithms are able to achieve similar results to MiCRO when applied under those same conditions. Furthermore, it would help researchers to design more challenging test cases for automated negotiation in which MiCRO is not optimal.

Analysis and Computation of the Outcomes of Pure Nash Equilibria in Two-Player Extensive-Form Games

Analysis and Computation of the Outcomes of Pure Nash Equilibria in Two-Player Extensive-Form Games

Cognitive hierarchies for games in extensive form

In the cognitive hierarchy (CH) framework, players in a game have heterogeneous levels of strategic sophistication. Each player believes that other players in the game are less sophisticated, and these beliefs correspond to the truncated distribution of a “true” distribution of levels. We develop the dynamic cognitive hierarchy (DCH) solution by extending the CH framework to games in extensive form. Initial beliefs are updated as the history of play provides information about players' levels of sophistication. We establish some general properties of DCH and fully characterize the DCH solution for a wide class of centipede games. DCH predicts a strategy-reduction effect: there will be earlier taking if the centipede game is played as an alternating-move sequential game rather than as a simultaneous move game in its reduced normal form. Experimental evidence reported in García-Pola et al. (2020a) supports this prediction. In all three centipede games for which the DCH strategy-reduction effect is predicted, termination occurs earlier when played sequentially rather than simultaneously with reduced strategies. In a fourth centipede game, where this effect is not predicted, it is not observed.

A game theory competitive intelligence solution stimulated from a Stackelberg game: A three players scenario

Competitive Intelligence (CI) involves systematically gathering information about the competitive landscape to anticipate rivals’ decisions and secure a strategic advantage. As academic interest in CI grows, the existing literature reflects a diverse body of knowledge. However, few works address the practical aspects of CI comprehensively, presenting viable solutions to its challenges. The motivation behind this paper is not only the scarcity of practical studies on CI but also the importance of CI and its benefits within companies, including improved decision-making and its positive impact on performance and sustainable growth. This study aims to contribute to the literature by proposing a CI solution grounded in game theory. We assert that applying game theory to CI is both intuitive and natural, given that the competitive environment readily lends itself to a game model. Viewing competitors as players, each striving to maximize profit, aligns seamlessly with game theory principles. We chose to consider a scenario with one initiator and multiple followers and model it as a Stackelberg game within the extensive form game framework. The literature review showed that the computational complexity of Stackelberg Equilibrium becomes NP-hard in most game classes with more than two players. This challenge encouraged us to contribute to the literature and focus on a scenario with two followers (three players), modeling the game in the extensive game form. To find a solution to this challenge, we used a modified version of the backward induction algorithm. To assess our solution’s efficacy, we conduct tests on 26 games (26 data instances), comparing results with those obtained using CPLEX and Decision Tree, and MiniMax methods. The ensuing pairwise sign test establishes the competitiveness of our outcomes. This research significantly contributes to the CI literature, offering a game theory-based solution and demonstrating its practical applicability through evaluation.

An extensive study of security games with strategic informants

Over the past years, game-theoretic modeling for security and public safety issues (also known as security games) have attracted intensive research attention and have been successfully deployed in many real-world applications for fighting, e.g., illegal poaching, fishing and urban crimes. However, few existing works consider how information from local communities would affect the structure of these games. In this paper, we systematically investigate how a new type of players – strategic informants who are from local communities and may observe and report upcoming attacks – affects the classic defender-attacker security interactions. Characterized by a private type, each informant has a utility structure that drives their strategic behaviors.For situations with a single informant, we capture the problem as a 3-player extensive-form game and develop a novel solution concept, Strong Stackelberg-perfect Bayesian equilibrium, for the game. To find an optimal defender strategy, we establish that though the informant can have infinitely many types in general, there always exists an optimal defense plan using only a linear number of patrol strategies; this succinct characterization then enables us to efficiently solve the game via linear programming. For situations with multiple informants, we show that there is also an optimal defense plan with only a linear number of patrol strategies that admits a simple structure based on plurality voting among multiple informants.Finally, we conduct extensive experiments to study the effect of the strategic informants and demonstrate the efficiency of our algorithm. Our experiments show that the existence of such informants significantly increases the defender's utility. Even though the informants exhibit strategic behaviors, the information they supply holds great value as defensive resources. Compared to existing works, our study leads to a deeper understanding on the role of informants in such defender-attacker interactions.

Selling Bonus Actions in Video Games

In the mobile video games industry, a common in-app purchase is for additional “moves” or “time” in single-player puzzle games. We call these in-app purchases bonus actions. In some games, bonus actions can only be purchased in advance of attempting a level of the game (pure advance sales (PAS)), yet in other games, bonus actions can only be purchased in a “spot” market that appears when an initial attempt to pass the level fails (pure spot sales). Some games offer both advance and spot purchases (hybrid advance sales). This paper studies these selling strategies for bonus actions in video games. Such a question is novel to in-app tools selling in video games, and it cannot be answered by previous advance selling studies focusing on end goods. We model the selling of bonus actions as a stochastic extensive form game. We show how the distribution of skill among players (i.e., their inherent ability to pass the level) and the inherent randomness of the game influence selling strategies. For casual games, where low-skill players have a sufficiently high probability of success in each attempt, if the proportion of high-skill players is either sufficiently large or sufficiently small, firms should adopt PAS and shut down the “spot” market. Furthermore, the player welfare-maximizing selling strategy is to sell only in the spot market. Hence, no “win-win” strategy exists for casual games. However, PAS can be a win-win for hardcore games, where low-skill players have a sufficiently low success probability for each attempt. This paper was accepted by Hemant Bhargava, information systems. Funding: C. T. Ryan received funding from NSERC Discovery [Grant RGPIN-2020-06488]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.02348 .

Autonomous Agent-Based Adaptation of Energy-Optimized Production Schedules Using Extensive-Form Games

Modular cyber-physical production systems are an important paradigm of Industry 4.0 to react flexibly to changes. The flexibility of those systems is further increased with skill-based engineering and can be used to adapt to customer requirements or to adapt manufacturing to disturbances in supply chains. Further potential for application of these systems can be found in the topic of electrical energy supply, which is also characterized by fluctuations. The relevance of energy-optimized production schedules for manufacturing systems in general becomes more important with the increased use of renewable energies. Nevertheless, it is often difficult to adapt when short-term energy price updates or unforeseen events occur. To address these challenges with an autonomous approach, this contribution focuses on extensive-form games to adapt energy-optimized production schedules in an agent-based manner. The paper presents agent-based modeling to transform and monitor energy-optimized production schedules into game trees to respond to changing energy prices and disturbances in production. The game is setup with a scheduler agent and energy agents who are considered players. The implementation of the mechanism is presented in two use cases, realizing decision making for an energy price update in a simulation example and for unforeseen events in a real-world demonstrator.

Iterated Admissibility does not Refine Extensive-form Rationalizability

Abstract I show that, in an extensive-form game, the outcomes that are consistent with iterated admissibility (i.e., with the iterated elimination of weakly dominated strategies) need not be consistent with extensive-form rationalizability.

Card Payment Protocol for Cryptocurrencies with Payment Channel Network

Cryptocurrency, despite the upsurge as a speculative investment, is still a long way from being people’s money. The extreme technicality poses a significant barrier for the general public to adopt it as a medium of exchange. Therefore, simplifying the payment process is a predominant necessity; for example, facilitation in adopting conventional payment instruments can bring convenience to both merchants and consumers. This paper proposes a novel cryptocurrency card payment protocol leveraging the Payment Channel Network (PCN) concept, facilitating high throughput and affordable transactions. Our design is based on the Bitcoin-backed Lightning Network (LN) with adjustments to make it executable by a smart card. It also preserves the decentralized nature of cryptocurrencies, reduces operational costs in several ways, and allows instant settlement for the recipients as compared to both conventional and cryptocurrency card payment systems. Our game theoretical analysis, where we model the engagement between the cardholder and the card agent as a long-run extensive form game, attests that they accord with the protocol without experiencing any honest loss under pragmatic conditions. We also discuss the privacy features compared to conventional card payments and LN. The protocol can function independently, without the need for trust, and can also be regulated for those seeking government mediation. This approach can potentially revolutionize the payment landscape by allowing the public to use cryptocurrency for everyday transactions conveniently and allowing existing cryptocurrency holders to conduct affordable micropayments.

Efficient Learning in Polyhedral Games via Best-Response Oracles

We study online learning and equilibrium computation in games with polyhedral decision sets, a property shared by normal-form games (NFGs) and extensive-form games (EFGs), when the learning agent is restricted to utilizing a best-response oracle. We show how to achieve constant regret in zero-sum games and O(T^0.25) regret in general-sum games while using only O(log t) best-response queries at a given iteration t, thus improving over the best prior result, which required O(T) queries per iteration. Moreover, our framework yields the first last-iterate convergence guarantees for self-play with best-response oracles in zero-sum games. This convergence occurs at a linear rate, though with a condition-number dependence. We go on to show a O(T^(-0.5)) best-iterate convergence rate without such a dependence. Our results build on linear-rate convergence results for variants of the Frank-Wolfe (FW) algorithm for strongly convex and smooth minimization problems over polyhedral domains. These FW results depend on a condition number of the polytope, known as facial distance. In order to enable application to settings such as EFGs, we show two broad new results: 1) the facial distance for polytopes in standard form is at least γ/k where γ is the minimum value of a nonzero coordinate of a vertex of the polytope and k≤n is the number of tight inequality constraints in the optimal face, and 2) the facial distance for polytopes of the form Ax=b, Cx≤d, x≥0 where x∈R^n, C≥0 is a nonzero integral matrix, and d≥0, is at least 1/(c√n), where c is the infinity norm of C. This yields the first such results for several problems such as sequence-form polytopes, flow polytopes, and matching polytopes.

Responsibility in Extensive Form Games

Two different forms of responsibility, counterfactual and seeing-to-it, have been extensively discussed in philosophy and AI in the context of a single agent or multiple agents acting simultaneously. Although the generalisation of counterfactual responsibility to a setting where multiple agents act in some order is relatively straightforward, the same cannot be said about seeing-to-it responsibility. Two versions of seeing-to-it modality applicable to such settings have been proposed in the literature. Neither of them perfectly captures the intuition of responsibility. The paper proposes a definition of seeing-to-it responsibility for such settings that amalgamate the two modalities. The paper shows that the newly proposed notion of responsibility and counterfactual responsibility are not definable through each other and studies the responsibility gap for these two forms of responsibility. It shows that although these two forms of responsibility are not enough to ascribe responsibility in each possible situation, this gap does not exist if higher-order responsibility is taken into account.

On the Outcome Equivalence of Extensive-Form and Behavioral Correlated Equilibria

We investigate two notions of correlated equilibrium for extensive-form games: the extensive-form correlated equilibrium (EFCE) and the behavioral correlated equilibrium (BCE). We show that the two are outcome-equivalent, in the sense that every outcome distribution achievable under one notion is achievable under the other. Our result implies, to our knowledge, the first polynomial-time algorithm for computing a BCE.

An Extensive-Form Game Paradigm for Visual Field Testing via Deep Reinforcement Learning.

Glaucoma is the leading cause of irreversible but preventable blindness worldwide, and visual field testing is an important tool for its diagnosis and monitoring. Testing using standard visual field thresholding procedures is time-consuming, and prolonged test duration leads to patient fatigue and decreased test reliability. Different visual field testing algorithms have been developed to shorten testing time while maintaining accuracy. However, the performance of these algorithms depends heavily on prior knowledge and manually crafted rules that determine the intensity of each light stimulus as well as the termination criteria, which is suboptimal. We leverage deep reinforcement learning to find improved decision strategies for visual field testing. In our proposed algorithms, multiple intelligent agents are employed to interact with the patient in an extensive-form game fashion, with each agent controlling the test on one of the testing locations in the patient's visual field. Through training, each agent learns an optimized policy that determines the intensities of light stimuli and the termination criteria, which minimizes the error in sensitivity estimation and test duration at the same time. In simulation experiments, we compare the performance of our algorithms against baseline visual field testing algorithms and show that our algorithms achieve a better trade-off between estimation accuracy and test duration. By retaining testing accuracy with reduced test duration, our algorithms improve test reliability, clinic efficiency, and patient satisfaction, and translationally affect clinical outcomes.

The Marriage Game Revisited: New Insights About Domestic Labor, Divorces and Men’s Expectations About Marriage

In the Marriage Game, women decide whether to get married and afterward men decide whether to cooperate in the domestic tasks. Then, if a husband is not cooperative, a wife can divorce or remain married. The sequence of decisions can be formalized as a game in extensive form, in which the strategic interaction between partners turns out evident. A husband may deceive, hoping that the divorce threat is not realistic, and a woman may decide not to get married from the beginning. If players had perfect knowledge about partners’ attitude, then divorce would not exist. Unfortunately, partners’ type is revealed only after the wedding. So, it is assumed that the game is played by different type of players, both men and women, and they interact with incomplete information. The model is solved by calculating all the perfect Bayes–Nash equilibria and it is shown that they depend on a complex interaction between model parameters, as multiple or mixed strategy equilibria can be found same parameters configuration. Comparing equilibria, we argue that the model can describe the marriage evolution that has been experienced by contemporary society. Following the increasing women’s participation in the job market, the number of marriages started to decline, but surprisingly, we are observing its resurgence in the most advanced societies. Our solution to the Marriage Game points to both the active role of autonomous women and the men’s expectations about marriage. As the number of autonomous women increases, men realize that divorce is credible and they change their expectations on women.

An Introduction to Game Theory

Game theory is a branch of mathematics and economics that offers a unique lens through which to analyze strategic interactions among rational decision-makers. This paper provides a concise introduction to the fundamental concepts and applications of game theory. It explores the core components of games, including players, strategies, and payoffs, and distinguishes between normal form and extensive form games. Key classic games, such as the Prisoner's Dilemma and the Nash Equilibrium, are discussed to illustrate core principles. The paper also highlights the diverse applications of game theory in economics, political science, biology, and psychology, showcasing its versatility as a tool for understanding human behavior and decision-making in various fields. Whether you are a student new to the subject or a professional seeking a refresher, this introduction to game theory lays the foundation for a deeper appreciation of strategic thinking and its real-world implications.

Optimal incentive design of pre-disaster urban planning based on location choice modeling with extensive-form game

Optimal incentive design of pre-disaster urban planning based on location choice modeling with extensive-form game

Partial observation learning-based task offloading and spectrum allocation in UAV collaborative edge computing

Capable of flexibly supporting diverse applications and providing computation services, the Mobile Edge Computing (MEC)-assisted Unmanned Aerial Vehicle (UAV) network is emerging as an innovational paradigm. In this paradigm, the heterogeneous resources of the network, including computing and communication resources, should be allocated properly to reduce computation and communication latency as well as energy consumption. However, most existing works solely focus on the optimization issues with global information, which is generally difficult to obtain in real-world scenarios. In this paper, fully considering the incomplete information resulting from diverse types of tasks, we study the joint task offloading and spectrum allocation problem in UAV network, where free UAV nodes serve as helpers for cooperative computation. The objective is to jointly optimize offloading mode, collaboration pairing, and channel allocation to minimize the weighted network cost. To achieve the purpose with only partial observation, an extensive-form game is introduced to reformulate the problem, and a regret learning-based scheme is proposed to achieve the equilibrium solution. With retrospective improvement property and information set concept, the designed algorithm is capable of combating incomplete information and obtaining more precise allocation patterns for diverse tasks. Numerical results show that our proposed algorithm outperforms the benchmarks across various settings.

Automated workflow generation supporting the value stream design of reconfigurable robot assembly cells

The paper addresses the automated generation of value stream optimized assembly workflows for reconfigurable robot cells. The focus is on the generation of asynchronous concurrent action workflows from assembly task descriptions. The main motivation is to enable automated search for optimized solutions within the enormous design spaces of these systems which results from their structural and procedural configurability. The proposed approach conducts task assignment, task sequencing and logical task planning (AI Planning) for multiple agents. The approach combines existing methods from the distinct research fields of robot task sequencing and discrete task planning. The contribution of the research is twofold. Firstly, the paper proposes a generic domain meta model enabling automated workflow generation for multi-agent assembly tasks. Secondly, a workflow generation approach based on artificial intelligence planning combined with the game-theoretic concept of extensive form games is presented. The approach iteratively generates a cooperative strategy for acting agents which is subsequently optimized in terms of individual strategies. The obtained logical action plans are further transformed into parametric concurrent action schedules to support downstream design activities. Both the meta model and the workflow generation approach are applied in a case study and provide valuable information on achievable assembly speedup.

Testing Game Theory of Mind Models for Artificial Intelligence

In this article, we investigate the relative performance of artificial neural networks and structural models of decision theory by training 69 artificial intelligence models on a dataset of 7080 human decisions in extensive form games. The objective is to compare the predictive power of AIs that use a representation of another agent’s decision-making process in order to improve their own performance during a strategic interaction. We use human game theory data for training and testing. Our findings hold implications for understanding how AIs can use constrained structural representations of other decision makers, a crucial aspect of our ‘Theory of Mind’. We show that key psychological features, such as the Weber–Fechner law for economics, are evident in our tests, that simple linear models are highly robust, and that being able to switch between different representations of another agent is a very effective strategy. Testing different models of AI-ToM paves the way for the development of learnable abstractions for reasoning about the mental states of ‘self’ and ‘other’, thereby providing further insights for fields such as social robotics, virtual assistants, and autonomous vehicles, and fostering more natural interactions between people and machines.