Showing papers on "Stochastic game published in 2023"

Data Offloading in UAV-Assisted Multi-Access Edge Computing Systems Under Resource Uncertainty

Abstract: In this paper, a novel data offloading decision-making framework is proposed, where users have the option to partially offload their data to a complex Multi-access Edge Computing (MEC) environment, consisting of both ground and UAV-mounted MEC servers. The problem is treated under the perspective of risk-aware user behavior as captured via prospect-theoretic utility functions, while accounting for the inherent computing environment uncertainties. The UAV-mounted MEC servers act as a common pool of resources with potentially superior but uncertain payoff for the users, while the local computation and ground server alternatives constitute safe and guaranteed options, respectively. The optimal user task offloading to the available computing choices is formulated as a maximization problem of each user’s satisfaction, and confronted as a non-cooperative game. The existence and uniqueness of a Pure Nash Equilibrium (PNE) are proven, and convergence to the PNE is shown. Detailed numerical results highlight the convergence of the system to the PNE in few only iterations, while the impact of user behavior heterogeneity is evaluated. The introduced framework’s consideration of the user risk-aware characteristics and computing uncertainties, results to a sophisticated exploitation of the system resources, which in turn leads to superior users’ experienced performance compared to alternative approaches.

Analytically pricing variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching

Abstract: This paper proposes a new model with a two-factor stochastic equilibrium volatility level that can be used to price variance and volatility swaps with nonlinear payoff. The adopted model uses the CIR process as the volatility process with the constant equilibrium level replaced with a stochastic one, and at the same time incorporates the regime switching mechanics in order to better describe the underlying price. To better understand how the introduced regime switching impacts both swap prices, we also conduct numerical experiments to compare our results with those obtained without regime switching.

Testing for Salience Effects in Choices under Risk

Abstract: We construct and run an experiment to test the most basic choice effect predicted by Salience Theory. Subjects allocate wealth between a risky and a safe investment. While we vary an apparent payoff ratio to influence salience, treatments have economically equivalent consequences. Most other theories of behavior then predict zero effect. Our experimental findings are strongly consistent with the behavioral implication of a continuous version of Salience Theory. We provide a novel structural estimate on the strength of salience. In our setting, increasing the relative payoff contrast by one percent is equivalent to an increased odds ratio by about 0.4 percent.

Equilibrium existence in games with ties

Abstract: We provide conditions that simplify applying Reny's (1999) better‐reply security to Bayesian games and use these conditions to prove the existence of equilibria for classes of games in which payoff discontinuities arise only at “ties.” These games include a general version of all‐pay contests, first‐prize auctions with common values, and Hotelling models with incomplete information.

A Network Solution to Robust Implementation: the Case of Identical but Unknown Distributions

Abstract: We study robust mechanism design in environments in which agents commonly believe that others’ types are identically distributed, but we do not assume that the actual distribution is common knowledge, nor that it is known to the designer. First, we characterize all incentive compatible transfers under these assumptions. Second, we characterize the conditions under which full implementation is possible via direct mechanisms, that only elicit payoff relevant information, and the transfer schemes which achieve it whenever possible. The full implementation results obtain from showing that the problem can be transformed into one of designing a network of strategic externalities, subject to suitable constraints which are dictated by the incentive compatibility requirements.

Mobile Devices Strategies in Blockchain-Based Federated Learning: A Dynamic Game Perspective

Abstract: Leveraging various mobile devices to train the shared model collaboratively, federated learning (FL) can improve the privacy and security of 6G communication. To economically encourage the participation of heterogeneous mobile devices, an incentive mechanism and a fair trading platform are needed. In this paper, we implement a blockchain-based FL system and propose an incentive mechanism to establish a decentralized and transparent trading platform. Moreover, to better understand the mobile devices’ behaviors, we provide economic analysis for this market. Specifically, we propose two strategy models for mobile devices, namely the discrete strategy model (DSM) and the continuous strategy model (CSM). Also, we formulate the interactions among the non-cooperative mobile devices as a dynamic game, where they adjust their strategies iteratively to maximize the individual payoff based on others’ previous strategies. We further prove the existence in Nash equilibrium (NE) of two different models and propose algorithms to achieve them. Simulation results demonstrate the convergence of the proposed algorithms and show that the CSM can effectively increase the mobile devices’ payoffs to 128.1 percent at most compared with DSM.

Coordination and free-riding problems in the provision of multiple public goods

Abstract: This study considers the twin problems of free riding and coordination failure, which are prevalent in the provision of multiple public goods with diminishing marginal returns. Specifically, we consider a game with two public goods, each of which has an upper bound of effective contribution. Any costly contributions beyond the upper bound are wasted. In this game, the payoff-sum maximizing Pareto-optimal outcome requires the sum of contributions by the group members to be equal to the upper bound of each public good, resulting in a coordination problem regarding who contributes to which public good. We theoretically and experimentally examine whether the provision of information on the values of the upper bounds helps overcome these problems and improves efficiency. Theoretical analysis predicts that this information will improve efficiency because it prompts efficiency-concerned individuals to match the upper bounds of each public good in equilibrium. The experimental results show countervailing effects of providing information; namely, it improves coordination but exacerbates the free-riding problem.

Expected subjective value theory (ESVT): A representation of decision under risk and certainty

Abstract: We present a descriptive model of choice derived from neuroscientific models of efficient value representation in the brain. Our basic model, a special case of Expected Utility Theory, can capture a number of behaviors predicted by Prospect Theory. It achieves this with only two parameters: a time-indexed “payoff expectation” (reference point) and a free parameter we call “predisposition”. A simple extension of the model outside the domain of Expected Utility also captures the Allais Paradox. Our models shed new light on the computational origins and evolution of risk attitudes and aversion to outcomes below reward expectation (reference point). It delivers novel explanations of the endowment effect, the observed heterogeneity in probability weighting functions, and the Allais Paradox, all with fewer parameters and higher descriptive accuracy than Prospect Theory.

Evolutionary game dynamics of cooperation in prisoner's dilemma with time delay.

Abstract: Cooperation is an indispensable behavior in biological systems. In the prisoner's dilemma, due to the individual's selfish psychology, the defector is in the dominant position finally, which results in a social dilemma. In this paper, we discuss the replicator dynamics of the prisoner's dilemma with penalty and mutation. We first discuss the equilibria and stability of the prisoner's dilemma with a penalty. Then, the critical delay of the bifurcation with the payoff delay as the bifurcation parameter is obtained. In addition, considering the case of player mutation based on penalty, we analyze the two-delay system containing payoff delay and mutation delay and find the critical delay of Hopf bifurcation. Theoretical analysis and numerical simulations show that cooperative and defective strategies coexist when only a penalty is added. The larger the penalty is, the more players tend to cooperate, and the critical time delay of the time-delay system decreases with the increase in penalty. The addition of mutation has little effect on the strategy chosen by players. The two-time delay also causes oscillation.

Report-Dependent Utility and Strategy-Proofness

Abstract: Despite the truthful dominant strategy, participants in strategy-proof mechanisms submit manipulated preferences. In our model, participants dislike rejections and enjoy the confirmation from getting what they declare desirable. Formally, the payoff from a match decreases in its position in the submitted ranking such that a strategic trade-off between preference intensity and match probability arises. This trade-off can trigger the commonly observed self-selection strategies. We show that misrepresentations can persist for arbitrarily small report-dependent components. However, honesty is guaranteed to be optimal if and only if there is no conflict between the quality and feasibility of a match. We substantiate the theory with already existing evidence and provide novel testable predictions. This paper was accepted by Yan Chen, behavioral economics and decision analysis. Funding: This work was supported by UniCredit and Universities Foundation [Modigliani Research Grant 2020/2021] and Deutsche Forschungsgemeinschaft [Grant 280092119]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4504 .

Pooling Agents for Customer-Intensive Services

Abstract: To Pool or Not to Pool? Analyzing Customer-Intensive Services with Strategic Agents In customer-intensive services where service quality increases with service time, service providers commonly pool their agents and give performance bonuses that reward agents for achieving greater customer satisfaction and serving more customers. Conventional wisdom suggests that pooling agents reduce customer wait time whereas performance bonuses motivate agents to produce high-quality services, both of which should boost customer satisfaction. However, in “Pooling Agents for Customer-Intensive Services,” Wang, Yang, Cui, Ülkü, and Zhou find that when agents act strategically, they may choose to speed up under pooling in an attempt to serve more customers, thus undermining service quality. If this happens, pooling can backfire and result in both lower customer satisfaction and agent payoff. Consequently, the researchers propose a simple practical solution to restore the efficiency of pooling. They propose pooling a portion of the performance bonuses (incentive pooling) in conjunction with pooling agents (operational pooling).

Smart Contracts and the Coase Conjecture

Abstract: This paper reconsiders the problem of a durable-good monopolist who cannot make intertemporal commitments. The buyer’s valuation is binary and his private information. The seller has access to dynamic contracts and, in each period, decides whether to deploy the previous period’s contract or to replace it with a new one. The main result of the paper is that the Coase conjecture fails: the monopo-list’s payoff is bounded away from the low valuation irrespective of the discount factor. (JEL D42, D82, D86, L12)

Pairwise Comparison Evolutionary Dynamics with Strategy-Dependent Revision Rates: Stability and $\delta$-Passivity

Abstract: We report on new sufficient conditions for the stability of evolutionary dynamics in population games. A large number of agents interact noncooperatively in a population game by selecting strategies based on their payoffs. Each agent is allowed to revise its strategy repeatedly with an average frequency referred to as the revision rate. We are interested in the case where an agent's current strategy influences directly the revision rate. Existing stability results for this case assume that a memoryless potential game generates the strategies' payoffs. This article extends these results to allow for payoff mechanisms that can be either dynamic or memoryless games that do not have to be potential. To make our analysis concrete, we assume that the agents' revision preferences follow a so-called pairwise comparison protocol. These protocols are ubiquitous because they operate fully decentralized and with minimal information requirements (they need to access only the payoff values, not the mechanism). We use a well-motivated example to illustrate an application of our framework.

Impact of individual sensitivity to payoff difference between individuals on a discrete-time imitation dynamics

Abstract: The impact of individual sensitivity to the difference between expected payoffs of individuals interacting in pairs on a discrete-time imitation dynamics was investigated, where the probability of mutual imitation between pairs of individuals is measured by the Fermi function. The main results show clearly that although the evolutionary stability of our model is independent of the individual sensitivity, the change of this sensitivity may profoundly affect the dynamical behavior of the system, for example, the periodic or chaotic fluctuations due to increased individual sensitivity. These results may be more helpful for us to understand the imitation dynamics in real systems.

(Not) Everyone Can Be a Winner – the Role of Payoff Interdependence for Redistribution

Abstract: How does payoff interdependence affect preferences for redistribution? We experimentally implement a zero-sum setting and one in which everyone can be simultaneously successful. Across these, we compare redistribution given an identical level of inequality. First, two subjects’ performances in a real-effort task translate into chances of winning a prize. Across treatments, we vary the interdependence of payoffs: either there is only a single prize or both subjects can potentially win a prize at the same time. Afterwards, a spectator can redistribute the prize money. If payoffs are not directly interdependent, the average amount redistributed decreases by 14-22%. In additional treatments, solely performance determines the prize allocation. Nevertheless, the impact of payoff interdependence remains unchanged. Comparing the settings with and without randomness, we find that its mere presence increases redistribution, even though there is no uncertainty about the (relative) performance of the two subjects.

The Mnemonomics of Contractual Screening

Abstract: In many markets, buyers sign advance contracts before actual decisions on transactions or consumptions are made. Therefore, a buyer may have private information on expected payoff at the contracting stage, and as time moves on, new information on other components of payoff may arrive. However, prior information can be losable, forgettable, or unattended. In this paper, we investigate how limited memory may influence the optimal design of contracts for sequential screening. Despite memory loss, the buyer can make ex post inference about her initially informed type from the chosen contract. As ex ante screening facilitates subsequent retrospection, the chosen contract can serve as a self-reminding instrument. This would yield an endogenous demand for separation in ex ante contract choice. In response, distortions in the optimal contract design can be either mitigated or intensified, leading to improved or undermined social welfare, respectively. As a result, the equilibrium buyer surplus can be higher than that under perfect memory. We also show that the buyer can exhibit the so-called flat-rate bias, even though her preference is time consistent and perfectly predicted. In addition, as memory can be perfectly recovered from the equilibrium contract choice, investing on any other memory-improving instrument is redundant. Moreover, the buyer’s demand for screening can induce her to choose dominated refund contract. Nevertheless, when dominance must be obeyed, the seller may offer a menu of refund contracts with two-way distortions. This paper was accepted by Matthew Shum, marketing. Funding: The financial support offered by the Hong Kong RGC General Research Fund [Grant 14500519] is acknowledged.

A Hierarchical Game-Theoretic Decision-Making for Cooperative Multiagent Systems Under the Presence of Adversarial Agents

Abstract: Underlying relationships among Multi-Agent Systems (MAS) in hazardous scenarios can be represented as Game-theoretic models. This paper proposes a new hierarchical network-based model called Game-theoretic Utility Tree (GUT), which decomposes high-level strategies into executable low-level actions for cooperative MAS decisions. It combines with a new payoff measure based on agent needs for real-time strategy games. We present an Explore game domain, where we measure the performance of MAS achieving tasks from the perspective of balancing the success probability and system costs. We evaluate the GUT approach against state-of-the-art methods that greedily rely on rewards of the composite actions. Conclusive results on extensive numerical simulations indicate that GUT can organize more complex relationships among MAS cooperation, helping the group achieve challenging tasks with lower costs and higher winning rates. Furthermore, we demonstrated the applicability of the GUT using the simulator-hardware testbed - Robotarium. The performances verified the effectiveness of the GUT in the real robot application and validated that the GUT could effectively organize MAS cooperation strategies, helping the group with fewer advantages achieve higher performance.

Application of fuzzy Malliavin calculus in hedging fixed strike lookback option

Abstract: In this paper, we develop a Malliavin calculus approach for hedging a fixed strike lookback option in fuzzy space. Due to the uncertainty in financial markets, it is not accurate to describe the problems of option pricing and hedging in terms of randomness alone. We consider a fuzzy pricing model by introducing a fuzzy stochastic differential equation with Skorohod sense. In this way, our model simultaneously involves randomness and fuzziness. A well-known hedging strategy for vanilla options is so-called $ \Delta $-hedging, which is usually derived from the Itô formula and some properties of partial differentiable equations. However, when dealing with some complex path-dependent options (such as lookback options), the major challenge is that the payoff function of these options may not be smooth, resulting in the estimates are computationally expensive. With the help of the Malliavin derivative and the Clark-Ocone formula, the difficulty will be readily solved, and it is also possible to apply this hedging strategy to fuzzy space. To obtain the explicit expression of the fuzzy hedging portfolio for lookback options, we adopt the Esscher transform and reflection principle techniques, which are beneficial to the calculation of the conditional expectation of fuzzy random variables and the payoff function with extremum, respectively. Some numerical examples are performed to analyze the sensitivity of the fuzzy hedging portfolio concerning model parameters and give the permissible range of the expected hedging portfolio of lookback options with uncertainty by a financial investor's subjective judgment.

Multi-heterogeneity public goods evolutionary game on lattice

Abstract: The topic of how cooperation emerges and develops in the real world has been intensively studied. Many mechanisms and models have been proposed to explain this complex phenomenon with the idealized assumption that all players are homogeneous or have little heterogeneity. This paper investigates the evolution of the public goods game with multiple heterogeneities. Roughly speaking, the quantity of investment (by a cooperator), penalty (received by a defector), or cost (paid by a punisher) is not fixed but depends on specific evolutionary situation. Moreover, heterogeneity is also introduced in aspiration payoff of each player for the strategy updating rule. Multi-heterogeneity makes the considered model more realistic. The simulation experiment shows that the combination of modified punishment mechanism and strategy updating rule can promote cooperation density in both the multi-heterogeneity and homogeneity models.