Payoff Mechanism Research Articles

Evolutionary public good games based on the long-term payoff mechanism in heterogeneous networks

Over the past two decades, it has been of great concern to solve the puzzle of social dilemmas in spatial public goods games. It has been demonstrated that the introduction of memory effects can effectively promote cooperative emergence to some extent. In this paper, we focus on the impact of scale-free and high aggregation properties on the public goods game of memory heterogeneous groups. Here, we propose an optimal strategy selection mechanism based on long-term historical payoffs. In our model, a memory loss function ω is introduced to characterize the memory length of players, and accordingly, pairs determine the optimal strategy by comparing historical gains for the next game cycle. Experiments conducted on scale-free networks and small world networks show that the strategy selection mechanism based on long-term payoff can keep the proportion of cooperators at a high level. In addition, this study demonstrates that the heterogeneity of memory length in the network promotes the enhancement of network reciprocity and robustness, which is beneficial to further reveal the mechanism of cooperative behaviour emergence in complex networks.

The Impact of Blockchain on Enterprises Sharing Real Data Based on Dynamic Evolutionary Game Analysis

The use of blockchain technology can ensure that data remains untampered with once it is on the chain. However, it doesn’t guarantee the authenticity of data before it enters the chain. In this study, we developed a three-party dynamic evolutionary game model involving core enterprises, small and medium-sized enterprises (SMEs), and financial institutions. Our findings indicate that a blockchain supply chain (BSC) generates more economic benefits than a traditional supply chain (TSC). We then built a dynamic evolutionary game model between core enterprises and SMEs, which revealed that SMEs are influenced by core enterprises and tend to adopt the action strategies of the latter. Additionally, we developed a dynamic evolutionary game model between core enterprises and financial institutions and compared the reward and punishment mechanisms with the synergy payoff mechanism. In the reward and punishment mechanisms, the game is a zero-sum game, where one party’s gains come at the expense of the other party. This mechanism has certain limitations and must meet specific conditions to improve the willingness of enterprises to share data. On the other hand, the synergy payoff mechanism enhances the authenticity of shared data by increasing the payoff for participants. When core enterprises play games with SMEs, the probability of core enterprises uploading real data and the distribution ratio of synergy payoff show an inverted U-shape. Similarly, core enterprises and financial institutions have comparable results in allocating synergy payoff. To leverage the synergy payoff mechanism, the distribution proportion of players participating in the synergy payoff should be considered fair. Finally, we validated our findings by simulating the models. If we can use blockchain technology to enhance the mutual trust between enterprises and banks, both banks and enterprises can achieve sustainable development.

Epidemic population games and evolutionary dynamics

We propose a system theoretic approach to select and stabilize the endemic equilibrium of an SIRS epidemic model in which the decisions of a population of strategically interacting agents determine the transmission rate. Specifically, the population’s agents recurrently revise their choices out of a set of strategies that impact to varying levels the transmission rate. A payoff vector quantifying the incentives provided by a planner for each strategy, after deducting the strategies’ intrinsic costs, influences the revision process. An evolutionary dynamics model captures the population’s preferences in the revision process by specifying as a function of the payoff vector the rates at which the agents’ choices flow toward strategies with higher payoffs. Our main result is a dynamic payoff mechanism that is guaranteed to steer the epidemic variables (via incentives to the population) to the endemic equilibrium with the smallest infectious fraction, subject to cost constraints. We use a Lyapunov function not only to establish convergence but also to obtain an (anytime) upper bound for the peak size of the population’s infectious portion.

A market for trading forecasts: A wagering mechanism

In many areas of industry and society, including energy, healthcare, and logistics, agents collect vast amounts of data that are deemed proprietary. These data owners extract predictive information of varying quality and relevance from data depending on quantity, inherent information content, and their own technical expertise. Aggregating these data and heterogeneous predictive skills, which are distributed in terms of ownership, can result in a higher collective value for a prediction task. In this paper, a platform for improving predictions via the implicit pooling of private information in return for possible remuneration is envisioned. Specifically, a wagering-based forecast elicitation market platform has been designed, in which a buyer intending to improve their forecasts posts a prediction task, and sellers respond to it with their forecast reports and wagers. This market delivers an aggregated forecast to the buyer (pre-event) and allocates a payoff to the sellers (post-event) for their contribution. A payoff mechanism is proposed and it is proven that it satisfies several desirable economic properties, including those specific to electronic platforms. Furthermore, the properties of the forecast aggregation operator and scoring rules are discussed in order to emphasize their effect on the sellers’ payoff. Finally, numerical examples are provided in order to illustrate the structure and properties of the proposed market platform.

The role of the preferred neighbor with the expected payoff on cooperation in spatial public goods game under optimal strategy selection mechanism

Cooperation is considered to be one of the driving forces to advance human civilization. How to increase the level of cooperation within the community has always been a hot research topic. Combining complex network theory and evolutionary game theory provides a practical, theoretical framework for investigating this problem. However, previous researchers often focused on the network models reflecting the real physical structures and the game models representing the social dilemmas. Few people paid attention to the role of the individual specific behaviors in the evolutionary game process. In this paper, we propose two mechanisms, “the preferred neighbor with the expected payoff” and “the optimal strategy selection mechanism based on historical information,” to emulate individual actions in the two stages of selecting learning targets and choosing strategies, respectively. The preferred neighbor with the expected payoff mechanism can select learning objectives purposefully, avoiding the blindness caused by random selection in previous studies. The optimal strategy selection mechanism determines the best strategy by comprehensively considering the strategies and payoffs in a given time dimension to be used for the next game round robin. The simulation results demonstrate that either of the above two mechanisms can significantly promote the level of cooperation. If they join forces, the cooperation level of the system can be maximized to the greatest extent. Our work may provide some new approaches to increasing the overall cooperation levels from a brand-new perspective.

The ABC mechanism: an incentive compatible payoff mechanism for elicitation of outcome and probability transformations

When it comes to experiments with multiple-round decisions under risk, the current payoff mechanisms are incentive compatible with either outcome weighting theories or probability weighting theories, but not both. In this paper, I introduce a new payoff mechanism, the Accumulative Best Choice (“ABC”) mechanism that is incentive compatible for all rational risk preferences. I also identify three necessary and sufficient conditions for a payoff mechanism to be incentive compatible for all models of decision under risk with complete and transitive preferences. I show that ABC is the unique incentive compatible mechanism for rational risk preferences in a multiple-task setting. In addition, I test empirical validity of the ABC mechanism in the lab. The results from both a choice pattern experiment and a preference (structural) estimation experiment show that individual choices under the ABC mechanism are statistically not different from those observed with the one-round task experimental design. The ABC mechanism supports unbiased elicitation of both outcome and probability transformations as well as testing alternative decision models that do or do not include the independence axiom.

An Enhanced Attribute Co‐evolutionary Game Reduction Algorithm by Integrating Self‐adaptive Multi‐level Nash Equilibrium

In order to further analyze the dynamical behavior of co-evolutionary populations in minimum attribute reduction, an Enhanced attribute co-evolutionary game reduction (EACGR) algorithm by integrating selfadaptive multi-level Nash equilibrium is proposed in this paper. First, a self-adaptive multi-level Nash game model with cross co-evolution is designed to provide the better solution for the dynamical symmetric co-evolution of multi-populations. Second, the profit matrix of elitist energy is constructed to explore the payoff mechanism of co-evolutionary selection. And then a novel Nash equilibrium strategy is adopted to perform attribute co-evolutionary game reduction so that the admissible balance of attribute reduction can be well achieved. Experimental results indicate that EACGR has the higher performance of minimum attribute reduction, and the application into 3D brain MRI segmentation with promising results indicates its stronger robustness and practicability.

THE BRITISH KNOCK-OUT PUT OPTION

Following the economic rationale introduced by Peskir & Samee (2011, 2013) we present a new class of barrier options within the British payoff mechanism where the holder enjoys the early exercise feature of American type options whereupon his payoff (deliverable immediately) is the best prediction of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Should the option holder believe the true drift of the stock price to be unfavorable (based upon the observed price movements) he can substitute the true drift with the contract drift and minimize his losses. In this paper, we focus on the knock-out put option with an up barrier. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results, we perform a financial analysis of the British knock-out put option. We spot some of the trends previously seen in Peskir & Samee (2011) but observe some behavior unique to the knock-out case. Finally, we derive the British put-call and up-down symmetry relations which express the arbitrage-free price and the rational exercise boundary of the British down-and-out call option in terms of the arbitrage-free price and the rational exercise boundary of the British up-and-out put option.

Paradoxes and mechanisms for choice under risk

Experiments on choice under risk typically involve multiple decisions by individual subjects. The choice of mechanism for selecting decision(s) for payoff is an essential design feature unless subjects isolate each one of the multiple decisions. We report treatments with different payoff mechanisms but the same decision tasks. The data show large differences across mechanisms in subjects' revealed risk preferences, a clear violation of isolation. We illustrate the importance of these mechanism effects by identifying their implications for classical tests of theories of decision under risk. We discuss theoretical properties of commonly used mechanisms, and new mechanisms introduced herein, in order to clarify which mechanisms are theoretically incentive compatible for which theories. We identify behavioral properties of some mechanisms that can introduce bias in elicited risk preferences-from cross-task contamination-even when the mechanism used is theoretically incentive compatible. We explain that selection of a payoff mechanism is an important component of experimental design in many topic areas including social preferences, public goods, bargaining, and choice under uncertainty and ambiguity as well as experiments on decisions under risk.

On the Payoff Mechanisms in Peer-Assisted Services With Multiple Content Providers: Rationality and Fairness

This paper studies an incentive structure for cooperation and its stability in peer-assisted services when there exist multiple content providers, using a coalition game theoretic approach. We first consider a generalized coalition structure consisting of multiple providers with many assisting peers, where peers assist providers to reduce the operational cost in content distribution. To distribute the profit from cost reduction to players (i.e., providers and peers), we then establish a generalized formula for individual payoffs when a "Shapley-like" payoff mechanism is adopted. We show that the grand coalition is unstable, even when the operational cost functions are concave, which is in sharp contrast to the recently studied case of a single provider where the grand coalition is stable. We also show that irrespective of stability of the grand coalition, there always exist coalition structures which are not convergent to the grand coalition under a dynamic among coalition structures. Our results give us an incontestable fact that a provider does not tend to cooperate with other providers in peer-assisted services, and be separated from them. Three facets of the noncooperative (selfish) providers are illustrated; (i) underpaid peers, (ii) service monopoly, and (iii) oscillatory coalition structure. Lastly, we propose a stable payoff mechanism which improves fairness of profit-sharing by regulating the selfishness of the players as well as grants the content providers a limited right of realistic bargaining. Our study opens many new questions such as realistic and efficient incentive structures and the tradeoffs between fairness and individual providers' competition in peer-assisted services.

The British call option

Alongside the British put option (Peskir and Samee [Appl. Math. Finance, 2011, 18, 537–563]) we present a new call option where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to the British call option. Should the option holder believe the true drift of the stock price to be unfavourable (based upon observed price movements) he can substitute the true drift with the contract drift and minimise his losses. The practical implications of this protection feature are most remarkable as not only can the option holder exercise at or below the strike price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favourable he will generally receive high returns. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterised as the unique solution to a nonlinear integral equation. In addition we derive the ‘British put–call symmetry’ relations which express the arbitrage-free price and the rational exercise boundary of the British call option in terms of the arbitrage-free price and the rational exercise boundary of the British put option where the roles of the contract drift and the interest rate have been swapped. These relations provide a useful insight into the British payoff mechanism that is of both theoretical and practical interest. Using these results we perform a financial analysis of the British call option that leads to the conclusions above and shows that with the contract drift properly selected the British call option becomes a very attractive alternative to the classic European/American call.

A systemic payoff in a self-repairing network

Cooperation among agents is a crucial problem in autonomous distributed systems composed of selfish agents pursuing their own profits. An earlier study of a self-repairing network revealed that a systemic payoff was able to make the selfish agents cooperate with others. The systemic payoff is a payoff mechanism that sums up not only an agent's own payoff, but also its neighborhood's payoff. In the systemic payoff, the distance effect between the agents has not yet been studied. This article considers the systemic payoff that involves the distance effect among agents. We studied the effectiveness of the proposed mechanism for the network performance by multi-agent simulations.

When a risky prospect is valued more than its best possible outcome

AbstractIn this paper, we document a violation of normative and descriptive models of decision making under risk. In contrast to uncertainty effects found by Gneezy, List and Wu (2006), some subjects in our experiments valued lotteries more than the best possible outcome. We show that the overbidding effect is more strongly related to individuals’ competitiveness traits than comprehension of the lottery’s payoff mechanism.

The role of role uncertainty in modified dictator games

We compare behavior in modified dictator games with and without role uncertainty. Subjects choose between a selfish action, a costly surplus creating action (altruistic behavior) and a costly surplus destroying action (spiteful behavior). While costly surplus creating actions are the most frequent under role uncertainty (64%), selfish actions become the most frequent without role uncertainty (69%). Also, the frequency of surplus destroying choices is negligible with role uncertainty (1%) but not so without it (11%). A classification of subjects into four different types of interdependent preferences (Selfish, Social Welfare maximizing, Inequity Averse and Competitive) shows that the use of role uncertainty overestimates the prevalence of Social Welfare maximizing preferences in the subject population (from 74% with role uncertainty to 21% without it) and underestimates Selfish and Inequity Averse preferences. An additional treatment, in which subjects undertake an understanding test before participating in the experiment with role uncertainty, shows that the vast majority of subjects (93%) correctly understand the payoff mechanism with role uncertainty, but yet surplus creating actions were most frequent. Our results warn against the use of role uncertainty in experiments that aim to measure the prevalence of interdependent preferences.

The effect of asymmetric payoff mechanism on evolutionary networked prisoner’s dilemma game

In social and biological systems, there are obvious individual divergence and asymmetric payoff phenomenon due to the strength, power and influence differences. In this paper, we introduce an asymmetric payoff mechanism to evolutionary Prisoner’s Dilemma Game (PDG) on scale-free networks. The co-effects of individual diversity and asymmetric payoff mechanism on the evolution of cooperation and the wealth distribution under different updating rules are investigated. Numerical results show that the cooperation is highly promoted when the hub nodes are favored in the payoff matrix, which seems to harm the interest of the majority. But the inequality of social wealth distribution grows with the unbalanced payoff rule. However, when the node difference is eliminated in the learning strategy, the asymmetric payoff rule will not affect the cooperation level. Our work may sharpen the understanding of the cooperative behavior and wealth inequality in the society.

The effect of the background risk in a simple chance improving decision model

We experimentally investigate the effect of an independent and exogenous background risk to initial wealth on subjects’ risk attitudes and explore an appropriate incentive mechanism when identical or similar tasks are repeated in an experiment. Taking a simple chance improving decision model under risk where the winning probabilities are negatively related to the potential gain, we find that such a background risk tends to make risk-averse subjects behave more risk aversely. Furthermore, we find that risk-averse subjects tend to show decreasing absolute risk aversion (DARA), and that a random round payoff mechanism (RRPM) would control the possible wealth effect. This suggests that RRPM would be a better incentive mechanism for an experiment where repetition of a task is used.