Maximum Payoff Research Articles

Dynamics of the full information minority game due to the agent’s impact

We propose the full information minority game (FIMG) in which agents perfectly recognize their impact on the market. For reflecting the impact of agents, we introduce an actual total action and an actual payoff which depend on the agent’s strategies. Unlike the perpetual fluctuating dynamics of the standard minority game, the dynamics of the FIMG settles into one of four steady states after a transient time. We classify steady states of the FIMG and analyze their characteristics. In most cases, the total payoff is maximized, and the total action settles into a periodic state. For measuring the degree of cooperation on the FIMG, we calculate a fraction of total payoff maximization and a mean relaxation time for the dynamics to settle into a steady state whose total payoff is maximized.

An MPS-BNS Mixed Strategy Based on Game Theory for Wireless Mesh Networks

To achieve a valid effect of wireless mesh networks against selfish nodes and selfish behaviors in the packets forwarding, an approach named mixed MPS-BNS strategy is proposed in this paper. The proposed strategy is based on the Maximum Payoff Strategy (MPS) and the Best Neighbor Strategy (BNS). In this strategy, every node plays a packet forwarding game with its neighbors and records the total payoff of the game. After one round of play, each player chooses the MPS or BNS strategy for certain probabilities and updates the strategy accordingly. In MPS strategy, each node chooses a strategy that will get the maximum payoff according to its neighbor's strategy. In BNS strategy, each node follows the strategy of its neighbor with the maximum total payoff and then enters the next round of play. The simulation analysis has shown that MPS-BNS strategy is able to evolve to the maximum expected level of average payoff with faster speed than the pure BNS strategy, especially in the packets forwarding beginning with a low cooperation level. It is concluded that MPS-BNS strategy is effective in fighting against selfishness in different levels and can achieve a preferable performance.

Optimal networks for quantum metrology: semidefinite programs and product rules

We investigate the optimal estimation of a quantum process that can possibly consist of multiple time steps. The estimation is implemented by a quantum network that interacts with the process by sending an input and processing the output at each time step. We formulate the search for the optimal network as a semidefinite program and use duality theory to give an alternative expression for the maximum payoff achieved by estimation. Combining this formulation with a technique devised by Mittal and Szegedy we prove a general product rule for the joint estimation of independent processes, stating that the optimal joint estimation can be achieved by estimating each process independently, whenever the figure of merit is of a product form. We illustrate the result in several examples and exhibit counterexamples showing that the optimal joint network may not be the product of the optimal individual networks if the processes are not independent or if the figure of merit is not of the product form. In particular, we show that entanglement can reduce by a factor K the variance in the estimation of the sum of K independent phase shifts.

Agency Problems in Venture Capital Contracts: Islamic Profit Sharing Ratio as a Screening Device

Both Islamic and classical venture contracts suffer from information asymmetry and incentive problems. Venture capitalist and Entrepreneur have an agency relationship because of the insufficient information about the funded project and/or the entrepreneur type. Referring to the literature, this paper presents a theory of Profit Sharing Ratio (PSR) for PLS contracts with adverse selection about the entrepreneur type. In order to avoid the agency problem, this paper proposes a theoretical framework in which the negotiated profit sharing ratio (PSR) acts as a screening device. We show that agency problems are signaled when the entrepreneur accepts a PSR set beyond a given threshold. This critical value of the PSR corresponds to the maximum payoff to the venture capitalist. We suggest that the optimal PSR level may complete the carried interest in classical venture contracts and offers a new tool for screening entrepreneurs’ type.

The Desire to Influence Others

We introduce the give-or-destroy game that allows us to fully elicit an individual’s social preference schedule. We find that about one third of the population exhibits both pro-social and anti-social preferences that are independent of payoff comparisons with those who are affected. We call this type of preference a desire to influence others. The other two thirds of the population consist to almost equal parts of payoff maximizers and pro-socials. Furthermore, we find that full information and experimenter demand may increase the extent of pro-social preferences, but neither treatment affects the extent of anti-social preferences or the distribution of social types in the population.

Optimal collusion under imperfect monitoring in multimarket contact

We investigate optimal collusion in repeated multimarket contact under imperfect public monitoring, where two firms operate in m markets and in each market, each firmʼs decision and public signals are binary. We show that in an optimal pure strategy strongly symmetric perfect public equilibrium, the size of efficiency loss is equal to that in the market with the most tempting deviation under single-market contact. Furthermore, we show a sufficient condition under which the symmetric equilibrium is optimal for joint payoff maximization among any perfect public equilibrium.

The Corporate Governance Role of Information Quality and Corporate Takeovers

We examine the corporate governance roles of firms' information quality and the takeover market in disciplining management. Increasing the information quality improves the takeover efficiency, but highly efficient takeover market also discourages the manager from working hard. We find that perfect information quality is not optimal for either the current shareholders' expected payoff maximization or the expected firm value maximization. The current shareholders' choice of information quality is different from the information quality level that maximizes the expected firm value, as the current shareholders only obtain a share of the value enhancement from a successful takeover, and moreover, the current shareholders also obtain an overbidding premium when the acquirer overbids for a low value firm. We also analyze the impact of antitakeover laws on firms' endogenous information quality as well as on the current shareholders' welfare and the firm value. We find that the expected firm value may increase after the adoption of antitakeover laws when the current shareholders are able to adjust their choice of information quality. This happens when the current shareholders increase the information quality in response to antitakeover laws.

Facing Your Opponents: Social Identification and Information Feedback in Contests

We experimentally investigate the effect of social identification and information feedback on individual behavior in contests. In all treatments we find significant over-expenditure of effort relative to the standard theoretical predictions. Identifying subjects through photo display decreases wasteful effort. Providing information feedback about others’ effort does not affect the aggregate effort, but it decreases the heterogeneity of effort and significantly affects the dynamics of individual behavior. A behavioral model which incorporates a non-monetary utility of winning and relative payoff maximization explains significant over-expenditure of effort. It also suggests that decrease in ‘social distance’ between group members through social identification promotes pro-social behavior and decreases over-expenditure of effort, while improved information feedback decreases the heterogeneity of effort.

No Need for Conspiracy: Self-Organized Cartel Formation in a Modified Trust Game

We investigate the dynamics of a trust game on a mixed population, where individuals with the role of buyers are forced to play against a predetermined number of sellers whom they choose dynamically. Agents with the role of sellers are also allowed to adapt the level of value for money of their products, based on payoff. The dynamics undergoes a transition at a specific value of the strategy update rate, above which an emergent cartel organization is observed, where sellers have similar values of below-optimal value for money. This cartel organization is not due to an explicit collusion among agents; instead, it arises spontaneously from the maximization of the individual payoffs. This dynamics is marked by large fluctuations and a high degree of unpredictability for most of the parameter space and serves as a plausible qualitative explanation for observed elevated levels and fluctuations of certain commodity prices.

The Impact of Imitation on Vaccination Behavior in Social Contact Networks

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity.

Learning efficient Nash equilibria in distributed systems

An individualʼs learning rule is completely uncoupled if it does not depend directly on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient (welfare-maximizing) pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: (i) the sum of payoffs over all agents, and (ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games.

Once Beaten, Never Again: Imitation in Two-Player Potential Games

We show that in symmetric two-player exact potential games, the simple decision rule imitate-if-better cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

On the Market Power of Network Coding in P2P Content Distribution Systems

Network coding is emerging as a promising alternative to traditional content distribution approaches in P2P networks. By allowing information mixture and randomized block selection, it simplifies the block scheduling problem, resulting in more efficient data delivery. Existing protocols have validated such advantages assuming altruistic and obedient peers. In this paper, we develop an analytical framework that characterizes a coding-based P2P content distribution market where rational agents seek for individual payoff maximization. Unlike existing game theoretical models, we focus on a decentralized resale market-through virtual monetary exchanges, agents buy the coded blocks from others and resell their possessions to those in need. We model such transactions as decentralized strategic bargaining games, and derive the equilibrium prices between arbitrary pairs of agents when the market enters the steady state. We further characterize the relations between coding complexity and market properties including agents' entry price and expected payoff, thus providing guidelines for strategic operations in a real P2P market. Our analysis reveals that the major power of network coding lies in maintaining stability of the market with impatient agents, and incentivizing agents with lower price and higher payoff, at the cost of reasonable coding complexity. Since the traditional P2P content distribution approach is a special case of network coding, our model can be generalized to analyze the equilibrium strategies of rational agents in decentralized resale markets.

Bounded rationality, strategy simplification, and equilibrium

It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization of strategy complexity, Rubinstein and co-authors studied forms of Nash equilibrium where strategies are maximally simplified in that no strategy can be further simplified without sacrificing payoff. Inspired by this line of work, we introduce a notion of equilibrium whereby strategies are also maximally simplified, but with respect to a simplification procedure that is more careful in that a player will not simplify if the simplification incents other players to deviate. We study such equilibria in two-player machine games in which players choose finite automata that succinctly represent strategies for repeated games; in this context, we present techniques for establishing that an outcome is at equilibrium and present results on the structure of equilibria.

Application of Markov Chains to Stock Trends

Problem statement: Modeling of the Dow Jones Industrial Average is frequently attempted in order to determine trading strategies with maximum payoff. Changes in the DJIA are important since movements may affect both individuals and corporations profoundly. Previous work showed that modeling a market as a random walk was valid and that a market may be viewed as having the Markov property. Approach: The aim of this research was to determine the relationship between a diverse portfolio of stocks and the market as a whole. To that end, the DJIA was analyzed using a discrete time stochastic model, namely a Markov Chain. Two models were highlighted, where the DJIA was considered as being in a state of (1) gain or loss and (2) small, moderate, or large gain or loss. A portfolio of five stocks was then considered and two models of the portfolio much the same as those for the DJIA. These models were used to obtain transitional probabilities and steady state probabilities. Results: Our results indicated that the portfolio behaved similarly to the entire DJIA, both in the simple model and the partitioned model. Conclusion: When treated as a Markov process, the entire market was useful in gauging how a diverse portfolio of stocks might behave. Future work may include different classifications of states to refine the transition matrices.

Extortion in the laboratory

Abstract In a laboratory experiment, we study a finitely repeated game ( T = 15) under complete information. In each round, P demands tribute (cash transfer) from A, A complies or refuses, and after refusals P may punish A. In equilibrium (payoff maximization), P does not punish and A refuses any positive demand. In the experiment, P punishes increasingly often and increasingly severely as she gains experience; most As comply with P’s demands. The observations are compatible with linear spite. In a finite mixture model, the types of P and A in the subject pool are characterized. An A that is resistant to extortion (declines all demands) is very rare, and hence the threat of punishment in general is effective, but all As either ignore actual punishment or react negatively to it. They accept to pay tribute but they are resistant to piecemeal expropriation.

Collusion-Resistant Reputation Mechanism for Multi-Agents Systems

Abstract We address the collusion problem in a reputation-driven multi-agent system where agents represent service providers, consumers, and a controller. A game structure is proposed where players are supposed rational and payoff maximizers. The main issue addressed in this paper is how to maintain a collusion-resistant reputation mechanism. We analyze the behavior of different players with respect to the strategies adopted by the opponents. We provide theoretical analysis of the game and discuss the pure and mixed strategy Nash equilibrium along with best response analysis to identify conditions under which the players adopt truthful dominant strategies.

Game Theoretic Approach for Enforcing Truth-Telling upon Relay Nodes

In this letter, an AGV based relay selection mechanism is developed to ensure relays reporting true information in wireless relay networks. The source selects relays based on the channel state information (CSI) of relay-destination links. Selfish relays may report fake CSI in order to obtain a better chance of being selected, whereas the source is not able to tell the reported in real or in false. In the proposed scheme, a relay node receives some payoffs from the destination with respect to the achievable data rate and also some compensations from the others in terms of the reported CSI of all relays. This mechanism not only enforces truth-telling upon relay nodes with maximum payoff but also ensures fairness among them. The equilibrium of payoff is attained when relay nodes report their true CSI. Simulation results demonstrate the theoretical solutions.

Who Cooperates in Repeated Games?

We explore the extent to which altruism, as measured by giving in a dictator game (DG), accounts for play in a noisy version of the repeated prisoner’s dilemma. We find that DG giving is correlated with cooperation in the repeated game when no cooperative equilibria exist, but not when cooperation is an equilibrium. Furthermore, none of the commonly observed strategies are better explained by inequity aversion or efficiency concerns than money maximization. Various survey questions provide additional evidence for the relative unimportance of social preferences. We conclude that cooperation in repeated games is primarily motivated by long-term payoff maximization and that even though some subjects may have other goals, this does not seem to be the key determinant of how play varies with the parameters of the repeated game. In particular, altruism does not seem to be a major source of the observed diversity of play.

On Delegation in Contests and the Survival of Payoff Maximizing Behavior

In two-player contests, optimal delegation involves giving the agent incentives to maximize the principal's payoff while in contests with more than two players incentives will be different from the principal's payoff maximization. These results are related to the evolutionary stability of payoff-maximizing preferences in the model of indirect evolution in general symmetric games, which depends on the slope of the reaction function being zero at equilibrium. Further examples of the relationship are also discussed.