Maximum Payoff Research Articles

Borrowing Absolute and Relative Gains to Science Diplomacy Conceptualization

Science diplomacy is an emerging concept in International Relations. But the existing traditional conceptualization of science diplomacy (science in diplomacy, diplomacy for science, and science for diplomacy) has optimistic scope and objective while ignoring the conflictual nature of international relations. This article argues borrowing relative and absolute gains can address the conceptual problem of science diplomacy. The borrowing presents a classification of science diplomacy into two types, prospective (using diplomacy to attain the maximum individual payoffs in science) and restrictive (using diplomacy to hinder others from advancing capabilities in science). By demonstrating it with Japan's science diplomacy in the inaugural meeting of Science and Technology in Society (STS) Forum and the first meeting of the East Asia Science and Innovation Area (e-ASIA) Joint Research Forum, this article found that the classification of science diplomacy as prospective and restrictive helps study the cooperative and competitive aspects of state actors' science diplomacy.

Indirect reciprocity undermines indirect reciprocity destabilizing large-scale cooperation

Previous models suggest that indirect reciprocity (reputation) can stabilize large-scale human cooperation [K. Panchanathan, R. Boyd, Nature 432, 499-502 (2004)]. The logic behind these models and experiments [J. Gross et al., Sci. Adv. 9, eadd8289 (2023) and O. P. Hauser, A. Hendriks, D. G. Rand, M. A. Nowak, Sci. Rep. 6, 36079 (2016)] is that a strategy in which individuals conditionally aid others based on their reputation for engaging in costly cooperative behavior serves as a punishment that incentivizes large-scale cooperation without the second-order free-rider problem. However, these models and experiments fail to account for individuals belonging to multiple groups with reputations that can be in conflict. Here, we extend these models such that individuals belong to a smaller, "local" group embedded within a larger, "global" group. This introduces competing strategies for conditionally aiding others based on their cooperative behavior in the local or global group. Our analyses reveal that the reputation for cooperation in the smaller local group can undermine cooperation in the larger global group, even when the theoretical maximum payoffs are higher in the larger global group. This model reveals that indirect reciprocity alone is insufficient for stabilizing large-scale human cooperation because cooperation at one scale can be considered defection at another. These results deepen the puzzle of large-scale human cooperation.

On Maximum Guaranteed Payoff in a Fuzzy Matrix Decision-Making Problem with a Fuzzy Set of States

The current study delves into a fuzzy matrix decision-making problem involving fuzzy sets of states. It establishes that a maximum guaranteed payoff constitutes a type-2 fuzzy set defined on the real line. Additionally, it provides the associated type-2 membership function. Moreover, the paper illustrates that the maximum guaranteed payoff type-2 fuzzy set of the decision-making problem can be broken down, based on the secondary membership grades, into a finite collection of fuzzy numbers. Each of these fuzzy numbers represents the maximum guaranteed payoff of the corresponding decision-making problem with a crisp set of states. This set corresponds to a specific cut of the original fuzzy set of states. Some properties of the maximum guaranteed payoff type-2 fuzzy set are investigated, and illustrative examples are provided. Since the problem formulation is symmetrical with respect to alternatives and states of nature, the results obtained can be used in the case of a fuzzy set of alternatives.

Networked Evolutionary Game-Based Demand Response via Feedback Controls

In this paper, the demand response considering interactive decision making between residential users and utility companies is modelled and controlled using networked evolutionary game (NEG) theory. The NEG is achieved via a widely used mathematical tool, namely the semi-tensor product (STP) of matrices, through which, feedback controls can be implemented to dynamically regulate the game-based networks. Firstly, the dynamic interactions between utility companies who provide various energy consumption packs and residential users who can intelligently choose preferable packs are modelled in the state-space form, in which both sides are consistently pursuing their maximum payoffs. Then, a quantitive analysis of such system’s equilibria is conducted using rigorous mathematical derivations, followed by the design of a profile feedback controller when the existing equilibria are not satisfactory towards the required energy consumption. Finally, an illustrative example is demonstrated, where the dynamic gaming between utility companies and users is illustrated and the effectiveness of the proposed feedback control is validated. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper addresses a very practical engineering problem, which is the demand response in the modern smart grid. Different from general optimization approaches in the existing works, the method proposed by this paper improves the demand response via feedback control of networked systems, which is based on the rigorous matrix approaches via state space equations. In addition, the work in this paper considers very practical factors in actual engineering (i.e., users with different action choices and decision logics being all together), which also provides much value to practitioners than the relevant works with similar theoretical approaches. The method proposed in this paper provides an effective regulation of the demand response in practice and can be flexibly adjusted according to actual situations.

A Subsidization Scheme for Maximizing Social Welfare in Mobile Communications Markets

In contemporary mobile communications markets, various agents or players interact to pursue welfare. Regulatory policies enacted by governments in certain markets aim to maximize social welfare. However, some countries, both least developed and developing, often adopt successful models from developed nations without local market validation. Therefore, network economics serves as a pertinent framework for analyzing such policies. This paper introduces a novel scheme based on constrained optimization problems, where the constraints represent multilevel economic game equilibria within a system model involving three agents: the central planner, the mobile network operator, and the mobile data users. These agents strategically optimize their payoff functions by considering benefit factors and decision variables such as the subsidization factor, pricing, and data consumption. To this end, a three-stage dynamic game is proposed to model the players’ interactions, employing the backward induction method to ascertain the subgame perfect equilibrium from the Nash equilibrium. A case study is presented, demonstrating a 31.16% increase in social welfare between scenarios involving no adoption of the subsidization factor and its adoption at the optimal value when the central planner enacts it to other players in the game, even if they do not necessarily attain maximum payoff values. In countries aligning with this proposed model, social welfare is maximized through a subsidization scheme.

Confusion cannot explain cooperative behavior in public goods games

Some scholars find that behavioral variation in the public goods game is explained by variations in participants' understanding of how to maximize payoff and that confusion leads to cooperation. Their findings lead them to question the common assumption in behavioral economics experiments that choices reflect motivations. We conduct two experiments, in which we minimize confusion by providing participants with increased training. We also introduce a question that specifically assesses participants' understanding of payoff maximization choices. Our experimental results show that the distribution of behavior types is significantly different when participants play with computers versus humans. A significant increase in contributions is also observed when participants play with humans compared to when they play with computers. Moreover, social norms may be the main motive for contributions when playing with computers. Our findings suggest that social preferences, rather than confusion, play a crucial role in determining contributions in public goods games when playing with humans. We therefore argue that the assumption in behavioral economics experiments that choices reveal motivations is indeed valid.

Information foraging with an oracle.

During ecological decisions, such as when foraging for food or selecting a weekend activity, we often have to balance the costs and benefits of exploiting known options versus exploring novel ones. Here, we ask how individuals address such cost-benefit tradeoffs during tasks in which we can either explore by ourselves or seek external advice from an oracle (e.g., a domain expert or recommendation system). To answer this question, we designed two studies in which participants chose between inquiring (at a cost) for expert advice from an oracle, or to search for options without guidance, under manipulations affecting the optimal choice. We found that participants showed a greater propensity to seek expert advice when it was instrumental to increase payoff (study A), and when it reduced choice uncertainty, above and beyond payoff maximization (study B). This latter result was especially apparent in participants with greater trait-level intolerance of uncertainty. Taken together, these results suggest that we seek expert advice for both economic goals (i.e., payoff maximization) and epistemic goals (i.e., uncertainty minimization) and that our decisions to ask or not ask for advice are sensitive to cost-benefit tradeoffs.

Game of strokes: Optimal & conversion strategy algorithms with simulations & application

Strategic decision-making for sequential move games requires rationality and continuity of rationality to guarantee maximum payoffs at all nodes/stages/levels. Rationality and continuity of rationality in a player's behaviour are not often observed and/or maintained thus, leading to less optimal outcomes. More so, the belief in an opponent's rationality, on the other hand, co-determines the level of effort a player employs while making strategic decisions. Given irrationality and discontinuity of rationality in a sequential move game with mover advantages, there are strategic steps (algorithms) to convert and/or maintain the mover advantages of an irrational player. In this paper, the conversion strategy algorithms, as well as the optimal strategy algorithms, are developed using the Beta Limit Sum (BLS) strategy model and the game of strokes. The simulation exercises confirm that the BLS strategy model is an optimal solution for the finite sequential game of strokes. One of the key applications of these strategies is that of resource economics like environmental resources (clean water, air & land). These are public goods, as such, the optimal strategy entails that the community cooperates (as one entity) and takes the same actions or strategy to maintain a healthy and clean state of the communal environmental resources.

China’s Policy Toward Afghanistan and Its Impact on India

The South Asia subcontinent is witnessing new security and political dynamics after the United States withdrew its troops in mid-2021. Even as the Taliban-led government is stepping up engagement with the outside world to earn wider diplomatic recognition and exhibit its governing credentials, Beijing and New Delhi are adjusting their regional policies in a bid to acquire more influence in a changing geopolitical landscape. Assuming nation states to be rational actors, this paper uses the stag hunt game to analyze the potential maximum payoffs for Beijing, Kabul, and New Delhi, respectively, if they could make the right strategic calculations about their short-term interests and long-term goals. Even though the subcontinent is not immune to the effect of great power rivalry that is unfolding on the world stage, regional stakeholders could still choose to cooperate on issues of common concern while limiting the fallout of competition and confrontation on other more contentious challenges.

The Conservatism Principle and Asymmetric Preferences over Reporting Errors

ABSTRACT Accounting conservatism has been described as deriving from preferences for reporting errors to be in the direction of understatement rather than overstatement. We pair reporters with users (who rely on reporters’ information) in a multiperiod experiment. We posit that, under misaligned incentives that motivate aggressive reporting, users view aggressive reports as reflecting exploitative intent and expect that a norm prohibiting aggressive reporting applies. We predict that users use noisy reporting errors to gauge reporters’ norm compliance. We find that, ceteris paribus, users prefer not to be paired with reporters producing overstatement errors likely to reflect aggressive reporting relative to reporters producing understatement errors likely to reflect conservative reporting; alternatively, we find no such asymmetric preferences when the agents’ motives are aligned. The asymmetric preferences cannot be explained by agency theory predictions of payoff maximization or loss aversion. These moral preferences provide an initial condition from which conservatism can endogenously emerge. Data Availability: Data are available from the authors upon request. JEL Classifications: B52; D81; D82; M41.

Theory of Cooperative Public Choice Games

This paper establishes an analytical framework for cooperative public choice games. In a cooperative public choice game under unanimity rule, all the players who belong to the only coalition will equally divide the cooperative payoff surplus, the equilibrium public choice is the one which can bring about the maximum cooperative payoff among all the public choices. In a cooperative public choice game under majority rule, compared with other public choices, the public choice with maximum comparative payoff will finally win the required majority of votes because of its greatest capability of attracting the intermediate team. When in a public choice game under majority rule there are more than two public choices which can bring about the maximum comparative payoff to the supporter coalition, the equilibrium choice will be the same one in the same public choice game under unanimity rule.

Peer-to-Peer Energy Trading through Swarm Intelligent Stackelberg Game

The development of smart grids has paved the way for sustainable energy infrastructure to transition towards decentralized energy trading. As intelligent agents, energy sources engage in energy trading based on their energy surplus or deficit. Buyers and sellers (participants) should achieve maximum payoffs in which buyers cut costs and sellers improve their utilities, and the security of sensitive information of smart agents must be guaranteed. This paper provides a blockchain-based energy trading network where intelligent agents can exchange energy in a secure manner, without the intervention of third parties. We model energy trading as a Stackelberg game, ensuring that the platform maximizes social welfare while participants increase their payoffs. Using the inherited characteristics of blockchain technology, a novel decentralized swarm intelligence technique is applied to solve the game while ensuring the privacy of the smart agents’ sensitive information. The numerical analysis demonstrates that the suggested method outperforms the present methods (Constant Utility Optimization, average method...) for optimizing the objectives of each agent by maximizing the sellers’ utilities and reducing the buyers’ costs. In addition, the experimental results demonstrate that it significantly reduces carbon footprint (15%) by enhancing energy exchange between intelligent agents.

The price of independence in a model with unknown dependence

How much does it cost a decisionmaker to base her payoff on interdependent, biased information sources? This question is relevant in economics, statistics, and politics. When there are many information sources, their dependence may be unknown or uncertain, which creates multivariate ambiguity. One approach to answer our leading question involves decoupling inequalities from probability theory. We present new inequalities which hold for any type of dependence. We apply our method to a simple formalization of risky asset investment, and to a voting model where citizens face dependent political signals. For a given set of marginal information, the decoupling bound is the sup over all possible joint distributions connecting the marginals. The bound may therefore be useful in other contexts, when a decisionmaker faces unawareness about the joint distribution of information. Our method highlights a frontier which bounds the maximum value of the decisionmaker’s payoff from dependent multidimensional signals. Beneath the bound lies the set of possible payoffs one could obtain from the signals. In this setting, decoupling performs a somewhat similar function to that of the threshold of acceptance sets, in choice under uncertainty. We show that a conservative decisionmaker’s maximal payoff is approximately 50% more than if the signals were independent.

Toward Zero-Determinant Strategies for Optimal Decision Making in Crowdsourcing Systems

The crowdsourcing system is an internet-based distributed problem-solving and production organization model, which has been applied in human–computer interaction, databases, natural language processing, machine learning and other fields. It guides the public to complete some tasks through specific strategies and methods. However, rational and selfish workers in crowdsourcing systems will submit solutions of different qualities in order to maximize their own benefits. Therefore, how to choose optimal strategies for selfish workers to maximize their benefits is important and crucial in such a scenario. In this paper, we propose a decision optimization method with incomplete information in a crowdsourcing system based on zero-determinant (ZD) strategies to help workers make optimal decisions. We first formulate the crowdsourcing problem, where workers have “winner-takes-all” rules as an iterated game with incomplete information. Subsequently, we analyze the optimal decision of workers in crowdsourcing systems in terms of ZD strategies, for which we find conditions to reach the maximum payoff of a focused worker. In addition, the analysis helps understand what solutions selfish workers will submit under the condition of having incomplete information. Finally, numerical simulations illustrate the performances of different strategies and the effects of the parameters on the payoffs of the focused worker.

Censorship and Reputation

I study how a firm manages its reputation by both investing in the quality of its product and censoring, hiding bad news from consumers. Without censorship, the threat of bad news provides strong incentives for investment. I highlight discontinuities in the firm’s maximum equilibrium payoff that censorship creates. When censorship is inexpensive, the firm never invests and a patient firm’s payoffs approach the lowest possible. In contrast, when censorship is moderately expensive, there exist equilibria where product quality is persistently high and payoffs approach the first-best, which can exceed the maximum equilibrium payoff if it was unable to censor. (JEL D21, D82, D83, G31, G32, L15)

Addressing the Dilemma of Online Gamification with Subgame Perfect Equilibria

Gamification, a concept originally derived from games, is defined as the extraction and inclusion of game mechanics within ordinary activities. Applying gamification to the educational context had surged over the past decade due to the recognition of the potential in motivating, promoting engagement, and enhancing student performance. The current study sought to overcome three dilemmas, including gamified depths, online gamification, and interaction, when gamifying the online learning environment through game theory, which investigates the arising conflict and collaboration among logical and intelligent decision-makers. This study used learning analytics based on the qualitative data collected from 57 undergraduates from the School of Educational Studies by exposing the students to gamified and non-gamified e-learning environments throughout eight weeks. By scrutinising the online gamification dilemma as a sequential game, the perfect equilibrium or Nash equilibrium at each subgame can be achieved using backward induction with synchronous online shallow gamification (4,6) and asynchronous online shallow gamification (3,5) as the optimal outcome. Hence, shallow gamification would allow players’ payoff maximization even when the asynchronous approach was selected, compared to asynchronous deep gamification.

Regret‐Minimizing Project Choice

An agent observes the set of available projects and proposes some, but not necessarily all, of them. A principal chooses one or none from the proposed set. We solve for a mechanism that minimizes the principal's worst‐case regret. We compare the single‐project environment in which the agent can propose only one project with the multiproject environment in which he can propose many. In both environments, if the agent proposes one project, it is chosen for sure if the principal's payoff is sufficiently high; otherwise, the probability that it is chosen decreases in the agent's payoff. In the multiproject environment, the agent's payoff from proposing multiple projects equals his maximal payoff from proposing each project alone. The multiproject environment outperforms the single‐project one by providing better fallback options than rejection and by delivering this payoff to the agent more efficiently.

Matching markets with middlemen under transferable utility

This paper studies matching markets in the presence of middlemen. In our framework, a buyer–seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer–seller pairs. For each such market, we examine the associated TU game. We first show that, in our context, an optimal matching can be obtained by considering the two-sided assignment market where each buyer–seller pair is allowed to use the mediation services of any middleman free of charge. Second, we prove that matching markets with middlemen are totally balanced: in particular, we show the existence of a buyer-optimal (seller-optimal) core allocation where each buyer (seller) receives her marginal contribution to the grand coalition. In general, the core does not exhibit a middleman-optimal allocation, not even when there are only two buyers and two sellers. However, we prove that in these small markets the maximum core payoff to each middleman is her marginal contribution. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors.

Collusion with capacity constraints under a sales maximization rationing rule

In the repeated Bertrand duopoly with capacity constraints, we introduce a sales maximization rationing rule, instead of a standard rationing rule, Efficient rule (E rule). Under our new rule, when the demand of a firm with a lower price exceeds its capacity, the consumers who are willing to buy at that price are rationed to that firm according to their unwillingness to buy. We find that the maximum one-shot total payoff under our rule is not less than that under E rule at any capacities; it is achieved by an asymmetric price pair rather than a symmetric monopoly price pair and it is strictly greater than that under E rule unless each firm’s capacity is too large. Under the one-shot total payoff maximization, total surplus under our rule is also equal to or greater than that under E rule at any capacities. Hence, our rule is also appealing to the social planner, and it is implementable due to information technology which collects information about the consumers’ willingness to pay. In the repeated game, patient firms can achieve the total payoff maximization by an equilibrium under our rule. Moreover, a range of discount factors within which the total payoff maximization can be sustained under our rule is wider than that under E rule at some capacities.

Managing product upgrades and rollover under demand uncertainty

We study the optimal product upgrades and rollover strategies of a risk-averse firm that is uncertain about future demand. For this purpose, we develop a two-period model based on whether the firm makes upgrading investments and if so which product rollover (solo or dual) strategy it adopts. Analysis of the equilibrium outcomes shows that if the firm is moderately risk-averse, it is unprofitable to upgrade and therefore only sells the first-generation product over two periods. Otherwise, the firm benefits from upgrading investments. In this case, the (solo-) dual-rollover guarantees the maximum total payoff if the degree of risk aversion is (low) high. Our sensitivity analysis demonstrates that: (i) the dual-rollover strategy can be seen as a hedge against increased demand uncertainty; (ii) the firm has a higher likelihood of using the dual-rollover strategy as cannibalization intensifies or intertemporal demand spillovers increase; and (iii) a lower payoff discount rate generally discourages the firm from upgrading the product. When upgrading investments happen, the optimal product rollover strategy is contingent upon the degree of risk aversion and the payoff discount rate.