Games Of Incomplete Information Research Articles

Modeling and optimization of networked evolutionary game based on incomplete information with switched topologies

AbstractIn the realm of evolutionary game theory, the majority of scenarios involve players with incomplete knowledge, specially regarding their opponents' actions and payoffs compounded by the ever‐shifting landscape of players' interactions. These dynamics present formidable challenges in both the analysis and optimization of game evolution. To address this, a novel model named the networked evolutionary game (NEG) is proposed based on incomplete information with switched topologies. This model captures situations where players possess limited insight into their opponents' benefits, yet make decisions based on their own payoffs while adapting to different networks and new players. To bridge the gap between incomplete and complete information games, R. Selten's transformation method is leveraged, a renowned approach that converts an incomplete information game into an interim agent game, thereby establishing the equivalence of pure Nash equilibria (NE) in both scenarios. Employing the semi‐tensor product (STP) of matrices, a powerful tool in logistic system, the evolution of the model is articulated through algebraic relationships. This enables to unravel the patterns of game evolution and identify the corresponding pure Nash equilibria. By introducing control players, strategically positioned within the game, optimized control is facilitated over the evolutionary trajectory, ultimately leading to convergence towards an optimal outcome. Finally, these concepts are illustrated with a practical example within the paper.

Welfare fragmented information effects: The cost-benefit analysis and Trade-offs

<p class="MsoNormal" style="margin-top: 12pt; text-align: justify;"><span lang="EN-US" style="font-family: 'times new roman', times, serif; font-size: 14pt;">We offer an extensive analysis of the significance of information within the realm of Gaussian quadratic economies. We build upon the seminal papers of Morris and Shin (2002, 2007) and consider a signal game of incomplete information. Particularly, we question the suitability of partial transparency portrayed by fragmented information in addition to the private signal in terms of welfare effects. We can summarize our findings in two main points. First, fragmented information, in conjunction with a private signal, can reduce the reliance on public signals. Second, a conflicting effect arises between increasing full disclosure and increasing the precision of fragmented (semi-public) information when examining different complex scenarios, involving for example endogenous private information or imperfect correlated signals. For a critical threshold, an optimal communication strategy designed by fragmented information should be implemented whenever that kind of information is acquired at a high precision.</span></p>

Quantile analysis of “hazard-rate” game models

This paper consists of an econometric analysis of a broad class of games of incomplete information. In these games, a player’s action depends both on her unobservable characteristic (the private information), as well as on the ratio of the distribution of the unobservable characteristic and its density function (which we call the ”hazard-rate”). The goal is to use data on players’ actions to recover the distribution of private information. We show that the structural parameter (the quantile of the unobservable characteristic, denoted by L) can be related to the reduced form parameter (the quantile of the data, denoted by Q) through a differential equation Q(α)=a(L(α),αL′(α)). We analyse the local and global identification of this equation in L. At the same time, under suitable assumptions, we establish the local and global well-posedness of the inverse problem Q=T(L). We solve the differential equation and, as a consequence of the well-posedness, we estimate nonparametrically the quantile and the c.d.f. function of the unobserved variables at a root-n speed of convergence (conditional on the quantile of the data being estimated at root-n). Moreover as the transformation of Q in L is continuous with respect to a topology that implies also the derivatives, we estimate nonparametrically the quantile density and the density the unobserved variables (that are continuous functions with respect to Q) at root-n speed of convergence. We provide also several generalisations of the model accounting for exogenuous variables, implicit expression of the strategy function and integral expression of the strategy function. Our results have several policy applications, including better design of auctions, regulation models, estimation of war of attrition in patent races, and public good contracts.

Maximizing Social Welfare and Agreement via Information Design in Linear-Quadratic-Gaussian Games

Information design in an incomplete information game involves a designer that aims to influence players' actions through signals generated from a designed probability distribution to optimize its objective function. For quadratic design objective functions, if the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, the information design problem is a semidefinite program (SDP) [1]. In this note, we seek to characterize the optimal information design analytically by leveraging the SDP formulation, when the design objective is to maximize social welfare or the agreement among players' action. We show that full information disclosure maximizes social welfare when there is a common payoff state, the payoff dependencies among players' actions are homogeneous, or when the signals are public. When the objective is to maximize the agreement among players' actions, not revealing any information is optimal. When the objective is a weighted combination of social welfare and agreement terms, we establish a threshold weight below which full information disclosure is optimal under public signals for games with homogeneous payoffs. Numerical results corroborate the analytical results, and identify partial information disclosure structures that are optimal.

Selling information in competitive environments

Data buyers compete in a game of incomplete information about which a single data seller owns some payoff-relevant information. The seller faces a joint information- and mechanism-design problem: deciding which information to sell, while eliciting the buyers' types and imposing payments. We derive the welfare- and revenue-optimal mechanisms for a class of games with binary actions and states. Our results highlight the critical properties of selling information in competitive environments: (i) the negative externalities arising from buyer competition increase the profitability of recommending the correct action to one buyer exclusively; (ii) for the buyers to follow the seller's recommendations, the degree of exclusivity must be limited; (iii) the buyers' obedience constraints also reduce the distortions in the allocation of information introduced by a monopolist; (iv) as competition becomes fiercer, these limitations become more severe, weakening the impact of market power on the optimal allocation of information.

Identification and estimation of sequential games of incomplete information with multiple equilibria

This paper discusses the identification and estimation of game-theoretic models, mainly focusing on sequential games of incomplete information. In most empirical games, researchers cannot observe the exact order of actions played in the game and rely on the assumption of simultaneous actions. My structural modeling generalizes an empirical game to encompass simultaneous and sequential actions as special cases. I specify a sequential game allowing for multiple players in each stage and multiple Perfect Bayesian Nash Equilibria, showing that the structural parameters, including the payoff function parameters, the order of actions, and the equilibrium selection mechanism, are separately identified. The various exclusion restrictions in the finite mixture literature help attain point identification of structural parameters and provide a testable method to verify identification conditions. Next, I consider a Sieve Minimum Distance (SMD) estimator of Ai and Chen (2003) for the structural parameters and verify its asymptotic properties. The Monte Carlo simulations evaluate the performance of the proposed estimator and provide numerical evidence of potential bias under the misspecified order of actions. The empirical application of Walmart and Kmart’s entry game demonstrates that retailers compete sequentially in a significant portion of markets.

Factors in Learning Dynamics Influencing Relative Strengths of Strategies in Poker Simulation

Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue to study poker by considering overarching strategies, namely rational and random play. In this work, a population of poker playing agents is instantiated to play the preflop portion of Texas Hold’em poker, with learning and strategy revision occurring over the course of the simulation. This paper aims to investigate the influence of learning dynamics on dominant strategies in poker, an area that has yet to be investigated. Our findings show that rational play emerges as the dominant strategy when loss aversion is included in the learning model, not when winning and magnitude of win are of the only considerations. The implications of our findings extend to the modeling of sub-optimal human poker play and the development of optimal poker agents.

Incentive-compatibility auction and renewable energy pricing strategy based on incomplete Information game of price cost declaration

ABSTRACT The construction and development of the Electricity Spot Market (ESM) are beneficial to the fair distribution of power resources and the improvement of power system regulation ability. The original ESM was not designed to include renewable energy. Since there is almost no marginal cost for renewable energy, the renewable energy can not copy the thermal power unit price model after participating in ESM. The prevalent Locational Marginal Price (LMP) mechanism within the extant ESM structure encounters limitations wherein optimal benefits accrue to buyers and sellers only under specific conditions. This paper thus introduces an innovative electricity pricing model and trading settlement strategy tailored to the characteristics of wind turbine-generated power. To begin, we devise a novel electricity pricing model grounded in the construction expenses and predictive precision intrinsic to renewable energy sources. Subsequently, in synergy with the ESM framework, we formulate a Bayesian game model to compute benefits contingent upon bid success probabilities. A pricing strategy based on Vickrey – Clarke – Groves (VCG) is selected, which pays the other generating strategy as an incremental cost by removing itself. Empirical evaluations affirm the efficacy and rationality of the proposed approach. The outcomes of our study not only validate its applicability but also lay the groundwork for a fresh theoretical paradigm underpinning energy trading modalities in future ESM contexts.

Persuading sincere and strategic voters

AbstractA sender wants to persuade multiple homogeneous receivers to vote in favor of a proposal. Before the vote sender commits to a signal which sends private, potentially correlated, messages to receivers that are contingent on the true state of the world. The best equilibrium for sender in the resulting incomplete information game is unappealing: all receivers vote in favor of sender's preferred outcome, irrespective of their message. We therefore focus on the equilibrium where receivers vote sincerely, that is they vote in favor of the outcome that is optimal given their posterior. We characterize the optimal public and the optimal private signal, both for the case where receivers are behavioral and vote sincerely as well as the case where such behavior is a Bayes–Nash equilibrium (BNE). For the optimal public signal, sincere voting is a BNE, but the optimal private signal is subject to the swing voter's curse. Imposing the constraint that sincere voting be a BNE leads to an optimal signal where receivers are never pivotal.

Stochastic Dynamic Information Flow Tracking game using supervised learning for detecting advanced persistent threats

Advanced persistent threats (APTs) are organized prolonged cyberattacks by sophisticated attackers with the intent of stealing critical information. Although APT activities are stealthy and evade detection by traditional detection tools, they interact with the system components to make progress in the attack. These interactions lead to information flows that are recorded in the form of a system log. Dynamic Information Flow Tracking (DIFT) has been shown to be an effective way to detect APTs using information flows. A DIFT-based detection mechanism dynamically performs security analysis on the information flows to detect possible attacks. However, wide range security analysis using DIFT results in a significant increase in performance overhead and high rates of false-positives and false-negatives. In this paper, we model the strategic interaction between APT and DIFT as a non-cooperative stochastic game. The game unfolds on a state space constructed from an information flow graph (IFG) that is extracted from the system log. The objective of the APT in the game is to choose transitions in the IFG to find an optimal path in the IFG from an entry point of the attack to an attack target. On the other hand, the objective of DIFT is to dynamically select nodes in the IFG to perform security analysis for detecting APT. Our game model has imperfect information as the players are unaware of the actions of the opponent. We consider two scenarios of the game (i) the false-positive and false-negative rates of DIFT (i.e., transition probabilities of the game) are known and (ii) the false-positive and false-negative rates are unknown. For case (i), we propose a value iteration-based algorithm and prove that the solution converges to the optimal solution (Nash equilibrium). Case (ii) translates to an incomplete information game with unknown transition probabilities. For case (ii), we propose a supervised learning-based algorithm, referred to as Hierarchical Supervised Learning (HSL) algorithm. HSL integrates a neural network, to predict the value vector of the game, with a policy iteration algorithm to compute an approximate equilibrium. We implemented our algorithms for cases (i) and (ii) on real attack datasets for nation state and ransomware attacks and validated the performance of our approach. We compared the performance of the HSL algorithm when the transition probabilities are unknown with instances with known transition probabilities and demonstrated that HSL algorithm converges to a solution close to optimal (i.e., optimal value vector) while the value vector obtained using greedy does not converge to optimal for 44.4% of the states and the mean absolute error is almost 200 times that of the HSL.

Boundedly rational bidding decision for land auctions during the transformation of real estate markets

Real estate developers in China exhibit different boundedly rational behaviors when bidding in different land auction formats, resulting in deviation from fully rational bidding, and the transformation of China’s real estate industry has intensified this deviation. To address this problem, this study establishes a reference utility model and a subjective decision probability model under the framework of incomplete information game to characterize developers’ utility distortion and winning probability distortion in open-bid auctions and sealed-bid auctions for land, respectively. The results show that the deviation between bounded rational bidding and fully rational bidding increases as developer competition intensifies. The equilibrium bidding of cost-disadvantaged developers in the boundedly rational model deviates less from the standard model. Moreover, in sealed-bid auctions, the "hiding degree" of cost-advantaged developers is greater, showing size effects, while the bids in open-bid auctions are more complex and affected by market conditions and developers’ risk preferences. Thus, this study characterizes boundedly rational bidding in land auctions and interprets the deviation from fully rational bidding, which can provide a more real basis for land auction mechanism design.

CompCube: A Space-Time-Request Resource Trading Framework for Edge-Cloud Service Market

As the footing stone of artificial intelligence (AI), ubiquitous computing resource is beginning to receive interest. With this trend, a new form of edge-cloud service market dedicated to collecting, trading, and scheduling computing resources is rising. The computing participants in the service market, as providers and demanders of computing resources, are becoming more diversified and open. As such, the intriguing economic phenomenon and the circulation mechanism have emerged. These bring inherent challenges, such as a volatile market, the ossification of pricing, isolation, and inefficiency. In this paper, we propose a novel space-time-request trading framework for the edge-cloud service market, namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CompCube</i> . To ensure stability, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CompCube</i> adopts the dual-circulation futures-spot trading method, including space-time dynamic pricing in the macro-cycle, request intention conversion, and resource matching in the micro-cycle. Among this, an incomplete information game model is designed to determine the long-term trading pricing in the macro-cycle. Then, to tackle the indicator isolation problem due to the inconsistency between the user's requests and the computing-power provider's (CPP's) resources, we focus on minimizing the rental cost of computing resources while satisfying diverse service level agreements (SLA) of users. To address this problem, a spatiotemporal scale Lyapunov optimization and an alternating actor-critic algorithm, A2SC, are developed. Besides, in the micro-cycle, a discriminatory double auction helps to determine the computing resource matching results efficiently and impersonally. We evaluate the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CompCube</i> of the A2SC algorithm with realistic datasets. Compared to other baselines, i.e., DYRECEIVE, Price Preferred, and Random, A2SC reduces the average rental cost by 30.45%, 5.74%, and 17.57%, respectively. Furthermore, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CompCube</i> can improve SLA satisfaction, as well as promote resource efficiency and social welfare compared with the traditional methods.

A small farmer’s market choice in the presence of multiple markets: The Indian case

We study a small farmer’s optimal market choice in the presence of multiple markets in an emerging economy. A small farmer sells her product through either of the three markets available: government-regulated market, corporate-owned market (a private market having high-quality requirements), and fixed-price market (a government procurement center). Using a dynamic game of incomplete information, we examine the impact of technology choice, quality effort, and yield quantity on the farmer’s market choice. We discuss the implications of the full information and asymmetric information case analysis with the help of real-life examples. We find out that the farmer does not put her optimal quality effort due to misalignment of stakeholder payoffs. We analytically prove that market inefficiency exists due to this misalignment; we subsequently propose that contract farming can eliminate this problem. We demonstrate that the corporate-owned and government-regulated markets have individual incentives to keep their markets segregated by maintaining different threshold quality requirements. We conduct a logistic regression analysis to explain the impact of various parameters on the small farmer’s market choice. It shows the impact of change in critical parameters on the small farmer’s optimal market choice. Our analysis allows policymakers to understand the behavior of small farmers as strategic players. Our study emphasizes the importance of the threshold quality requirement of markets and prices offered in these markets on a small farmer’s market choice rather than traditional factors such as transportation cost and minimum support price. We conduct field interviews of small farmers to augment our findings.

Information spillover in multiple zero-sum games

This paper considers an infinitely repeated three-player zero-sum game with two-sided incomplete information, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a generalization of the model in Aumann et al. (Repeated games with incomplete information. MIT Press, New York, 1995) of two-player zero-sum one-sided incomplete information games. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his long-term average payoffs (i.e., undiscounted payoffs). Our objective is to understand the adverse effects of “information spillover” from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects and characterize equilibrium payoffs. In a second result, we show how the effects of information spillover on the equilibrium payoff set of the informed player might be severe. Finally, we compare our findings on the equilibrium-payoff set of the informed player with those of Bayesian Persuasion models with multiple receivers.

Bargaining game based on psychological cost of electric vehicles and risk assessment of aggregators

AbstractAs electric vehicles (EVs) begin to participate in the peak‐shaving auxiliary service market, the question of how price aggregators can maximize the peak‐shaving capacity provided by EVs and maximize their own profit has become a major problem. This paper proposes a bargaining game pricing method based on the psychological cost of EVs and the risk assessment of aggregators. First, the comprehensive psychological cost of EV users is obtained based on the impact of users’ participation in peak shaving on the battery life of EVs and on users’ original travel plans and time, and the impact of aggregator pricing on users’ psychology. Then, based on users’ psychological cost and the law of gravitation, the evaluation scheme for the peak‐shaving capacity of EVs is obtained. On the basis of conditional value at risk (CVaR), the mixed CVaR is obtained by considering the risk‐chasing behaviour of users. Based on the mixed CVaR, the risk assessment of aggregators’ participation in the peak‐shaving auxiliary service market is carried out. According to the above information, the aggregator and EV groups are engaged in a bargaining game based on the peak‐shaving pricing problem, which is divided into complete information game and incomplete information game. Finally, the feasibility of the proposed method is verified by an example analysis which is run by the MATLAB R2019b. The method proposed in this paper provides aggregators with a complete peak‐shaving electricity pricing scheme, effectively improving the dispatching capacity of EVs. It is helpful to rationalize the pricing of aggregators and maximize their profits. EVs can also obtain satisfactory profits, attracting more EVs to participate in peak shaving, and reduce the pressure on power grid peak shaving.

SHARP TEST FOR EQUILIBRIUM UNIQUENESS IN DISCRETE GAMES WITH PRIVATE INFORMATION AND COMMON KNOWLEDGE UNOBSERVED HETEROGENEITY

This paper proposes a test of the single equilibrium in the data assumption commonly maintained when estimating static discrete games of incomplete information. By allowing for discrete common knowledge payoff-relevant unobserved heterogeneity, the test generalizes existing methods attributing all correlation between players’ decisions to multiple equilibria. It does not require the estimation of payoffs and is therefore useful in empirical applications leveraging multiple equilibria to identify the model’s primitives. The procedure boils down to testing the emptiness of the set of data generating processes that can rationalize the sample through a single equilibrium and a finite mixture over unobserved heterogeneity. Under verifiable conditions, this testable implication is generically sufficient for degenerate equilibrium selection. The main identifying assumption is the existence of an observable variable that plays the role of a proxy for the unobservable heterogeneity. Examples of such proxies are provided based on empirical applications from the existing literature.

Multi-echelon supply chain coordination: Contract sequence and cut-off policies

The influence of contract sequence and interaction between different contract mechanisms on profit allocation among supply chain agents and cutoff policies of a multi-echelon supply chain have received scarce consideration in the literature. In this study, we try to fill this gap and examine a serial decentralized three-echelon supply chain using a dynamic game of incomplete information where the supplier and the manufacturer can choose either a short-term contract or a long-term contract. Using two sequential bilateral monopoly settings we analyze four scenarios of contract sequence for calculating the payoffs of supply chain agents. Based on these payoffs, we calculate the Bayesian Nash equilibrium of the game. This study shows the importance of contract sequence in profit allocation among different stakeholders of a decentralized multi-echelon supply chain. We further demonstrate that the upstream agent does not necessarily hold higher bargaining power among all the agents. Our key findings are as follows: first, optimal profit levels, as well as cutoff policies, are influenced by marginal costs and reservation profits of supply chain agents along with contract sequence; second, supply chain coordination is dependent on contract sequence; third, supply chain agents do not naturally choose channel coordinating contract sequence; fourth, the supplier needs to devise incentive scheme for the manufacturer to coordinate the overall supply chain; fifth a myopic supplier prefers short-term agreement and a foresighted supplier prefers long-term agreement.

TESTING A CLASS OF SEMI- OR NONPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS USING SERIES METHODS

This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a parametric model for the conditional mean. Estimating conditional expectations using series methods and employing a Gaussian multiplier bootstrap to obtain critical values, the test is shown to be asymptotically correctly sized and consistent. Simulation studies indicate good finite-sample properties. In an empirical application, the test is used to study the validity of a game-theoretical model for discount store market entry, treating equilibrium beliefs as nonparametric conditional expectations. The test indicates that Walmart and Kmart entry decisions do not result from a static discrete game of incomplete information with linearly specified profits.

Modeling threats and promises: Explaining the Munich crisis of 1938

The use of an incomplete information game model to explore the strategic characteristics of the carrot and stick approach to coercive diplomacy shows that the dynamics of this manipulative bargaining tactic are much more nuanced than standard atheoretical accounts suggest. One unexpected finding is that when information is incomplete, there always exists a deterrence equilibrium under which no attempt is made to overturn the status quo. An all-out conflict or an unsuccessful fait accompli is also possible, but only when information about preferences is not common knowledge. Incomplete information, then, is a double-edged sword, sometimes enhancing the prospects for peace and at other times making conflict more likely. We use a special case of the Carrot and Stick Game model to shed theoretical light on the Munich crisis of 1938, a manufactured crisis if there ever was one. Hitler’s last-minute about-face was motivated by his newfound belief that the British, French, and Czechs intended to resist his planned military invasion of the Sudetenland and his preference to avoid an all-out war. While his preference was unchanged in 1939, his beliefs were not; as our model suggests, the consequences were more than predictable.

Reciprocity with uncertainty about others

We introduce the uncertainty of psychological motivation into a reciprocity model and explore its implications on behavior. More precisely, we assume that reciprocity sensitivities are subject to incomplete information and extend the Sequential Reciprocity Equilibrium in extensive-form games (Dufwenberg and Kirchsteiger, 2004) to a broader class of incomplete information games. We use this general framework to study many well-known games and find that uncertainty could either mitigate or strengthen players' reciprocal behavior. We investigate how uncertainty changes the equilibrium predictions of the standard reciprocity model and compare two setups in which the psychological motivations are known and unknown among the players, respectively. In particular, we find that, in the prisoners' dilemma, players are more likely to cooperate with each other when they have information about the reciprocal motivations of their opponents, given that the benefits of defection are modest.