Total Payoff Research Articles

Leadership scenarios in prisoner’s dilemma game

The prisoner’s dilemma game is the most known contribution of game theory into social sciences. Here we describe new implications of this game for transactional and transformative leadership. While the autocratic (Stackelberg’s) leadership is inefficient for this game, we discuss a Pareto-optimal scenario, where the leader L commits to react probabilistically to pure strategies of the follower F, which is free to make the first move. Offering F to resolve the dilemma, L is able to get a larger average pay-off. The exploitation can be stabilized via repeated interaction of L and F, and turns to be more stable than the egalitarian regime, where the pay-offs of L and F are equal. The total (summary) pay-off of the exploiting regime is never larger than in the egalitarian case. We discuss applications of this solution to a soft method of fighting corruption and to modeling the Machiavellian leadership. Whenever the defection benefit is large, the optimal strategies of F are mixed, while the summary pay-off is maximal. One mechanism for sustaining this solution is that L recognizes intentions of F.

Accelerating the adoption of automated vehicles by subsidies: A dynamic games approach

Early deployment of automated vehicles (AVs) may likely cause a loss of efficiency in the transportation system. However, after there are a sufficient number of such vehicles in the traffic stream, many benefits can be realized. It thus appears sensible to provide subsidies to promote the early adoption of AVs and shorten the transition period. This paper investigates an optimal subsidy policy that accelerates the deployment of AVs from lower to higher market penetration rates. The policy can maximize the government agency’s expected total payoff associated with the AV deployment. The main contribution is a dynamic games approach that considers the uncertainty in the market forecast and the information asymmetry between the government agency and the subsidized entities.

Money Maker or Penny Pincher: On the Psychological Foundation of Poverty Traps

We provide a new perspective to understand poverty traps by researching the effect of psychological poverty on economic decisions. Our innovative sample consists of two pools of subjects: impoverished students and normal students from the same university. Subjects were first randomly assigned either to a treatment group that induced them to think about finances or to a control group. Then all subjects performed three tasks of economic decisions. Our results show that priming in general significantly intensifies the poor’s choices, with fewer total payoffs, higher response times, and favoring “pinching pennies” over “making money,” all of which can perpetuate poverty traps.

Strategic Prosumers: How to Set the Prices in a Tiered Market?

We consider users who may have renewable energy harvesting devices or distributed generators. Such users can behave as consumers or producers (hence, we denote them as prosumers) at different time instances. We consider a tiered market where the grid selects a price function, which reveals price in the real time based on the total demand to the grid. In the real time, a prosumer can buy from another prosumer in an exchange market knowing the price from the grid. The exchange price is set by a platform and can be different for different sellers. A prosumer is a selfish entity, which selects the amount of energy it wants to buy either from the grid or from other prosumers or the amount of excess energy it wants to sell to other prosumers by maximizing its own payoff. However, the strategy and the payoff of a prosumer inherently depend on the strategy of other prosumers as a prosumer can only buy if the other prosumers are willing to sell. We formulate the problem as a coupled constrained game and seek to obtain the generalized Nash equilibrium. We show that the game is a concave potential game and show that there exists a unique generalized Nash equilibrium. We propose a distributed algorithm that converges to the exchange price, which clears the market and achieves the generalized Nash equilibrium. We, finally, show how the grid should select the price function in a day-ahead scenario by computing the estimated demand from the history. Our numerical result shows that the tiered market can reduce the peak load and increase the prosumers’ total payoffs.

On the Solution of a Differential Game of Managing the Investments in an Advertising Campaign

We consider a differential game of managing the investments in an advertising campaign for the case of n symmetric players. The problem is solved in the class of positional strategies both for the cooperative statement, where the players agree on using controls that maximize the total payoff before the game starts, and for the noncooperative statement, in which the Nash equilibrium is used as a solution. It is shown that the solution of the problem is not unique in both cases. One candidate function is found by means of a detailed analysis. Then the solution is chosen with the use of an economic criterion described by Bass et al. in 2005. The solutions chosen earlier are in complete agreement with the choice with respect to the economic criterion.

Bandits and Experts in Metric Spaces

In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is well understood, bandit problems with large strategy sets are still a topic of active investigation, motivated by practical applications, such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions that enable the design of efficient solutions. In this work, we study a general setting for the multi-armed bandit problem, in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the Lipschitz MAB problem . We present a solution for the multi-armed bandit problem in this setting. That is, for every metric space, we define an isometry invariant that bounds from below the performance of Lipschitz MAB algorithms for this metric space, and we present an algorithm that comes arbitrarily close to meeting this bound. Furthermore, our technique gives even better results for benign payoff functions. We also address the full-feedback (“best expert”) version of the problem, where after every round the payoffs from all arms are revealed.

Democracy matters: a psychological perspective on the beneficial impact of democratic punishment systems in social dilemmas

The implementation of punishment has proven a prominent solution to prevent the breakdown of cooperation in social dilemma situations. In fact, numerous studies show that punishment possibilities are effective in maintaining cooperative behavior. However, punishment is often not efficient in terms (a) of monetary benefits and in light of the fact (b) that punishment of cooperators (i.e., antisocial punishment) can occur. Still, recent research revealed that individuals vote for the implementation of such punishment systems. We address this contradiction by proposing that the benefits of democratic punishment systems in particular cannot be solely captured by monetary outcomes. Instead, the implementation of democratic punishment systems may enhance the psychological benefits of justice perceptions, satisfaction, and trust. Using iterated public goods games, the findings of the present study reveal not only higher cooperation levels and total payoffs in two different democratic punishment systems compared to other systems, but also higher justice perception, satisfaction, and trust. Furthermore, participants indicated the highest willingness to continue interactions in democratic punishment systems. Moreover, satisfaction, not monetary outcomes, was the best predictor of participants’ willingness to stay in a system. Therefore, we argue that the efficiency of democratic punishment systems cannot be measured solely in monetary outcomes but that psychological benefits must be considered.

Tauberian Theorem for Games with Unbounded Running Cost

We study two game families with total payoffs that are defined either as the Cesaro average (the long run average game family) or Abel average (the discounting game family) of the running costs. We study value functions for all sufficiently small discounts and for all sufficiently large planning horizons (asymptotic approach), investigate a robust strategy that provides a near-optimal total payoff in this case (uniform approach). Assuming the Dynamic Programming Principle, we prove the corresponding Tauberian theorems without requiring the boundedness of the running cost.

User-centric resource allocation with two-dimensional reverse pricing in mobile communication services

Reverse pricing has been recognized as an effective tool to handle demand variability and uncertainty in the travel industry (e.g., airlines and hotels). To investigate its viability in mobile communication services, as a benchmark case, we first consider that a single mobile network operator (MNO) adopts (MNO-driven) forward pricing only, taking into account heterogeneous and stochastic user demands. To effectively deal with the drawbacks of forward pricing only, we propose (user-driven) two-dimensional reverse pricing on top of forward pricing and design a ξ-approximate polynomial-time algorithm that can maximize the revenue of the MNO. Through analytical and numerical results, we show that the proposed scheme can achieve solutions: Higher average network capacity utilization, the increase in the average revenue of the MNO, and the increment in the total average payoff of the users. To verify its feasibility in practice, we further implement its real prototype and perform experimental studies. We show that the proposed scheme still creates triple-win solutions in practice. Our findings provide a new outlook on resource allocation, and design guidelines for adopting two-dimensional reverse pricing on top of forward pricing.

On the unprofitability of buyer groups when sellers compete

We study how the formation of a buyer group affects buyer power when sellers compete and buyers operate in separate markets. Previous research (Inderst and Shaffer, 2007, and Dana, 2012) has considered a buyer group that can commit to an exclusive purchase and has found that the formation of a buyer group strictly increases buyer power unless buyers have identical preferences. In contrast, we assume that no commitment to exclusive purchases is possible. We find that the formation of a buyer group has no effect if each seller's cost function is concave. If it is strictly convex, the buyer group strictly reduces the buyers' total payoff as long as the Pareto-dominant equilibrium for sellers is played when a buyer group is formed.

To vaccinate or not to vaccinate: A comprehensive study of vaccination-subsidizing policies with multi-agent simulations and mean-field modeling

We combined the elements of evolutionary game theory and mathematical epidemiology to comprehensively evaluate the performance of vaccination-subsidizing policies in the face of a seasonal epidemic. We conducted multi-agent simulations to, among others, find out how the topology of the underlying social networks affects the results. We also devised a mean-field approximation to confirm the simulation results and to better understand the influences of an imperfect vaccine. The main measure of a subsidy’ performance was the total social payoff as a sum of vaccination costs, infection costs, and tax burdens due to the subsidy. We find two types of situations in which vaccination-subsidizing policies act counterproductively. The first type arises when the subsidy attempts to increase vaccination among past non-vaccinators, which inadvertently creates a negative incentive for voluntary vaccinators to abstain from vaccination in hope of getting subsidized. The second type is a consequence of overspending at which point the marginal cost of further increasing vaccination coverage is higher than the corresponding marginal cost of infections avoided by this increased coverage. The topology of the underlying social networks considerably worsens the subsidy's performance if connections become random and heterogeneous, as is often the case in human social networks. An imperfect vaccine also worsens the subsidy's performance, thus narrowing or completely closing the window for vaccination-subsidizing policies to beat the no-subsidy policy. These results imply that subsidies should be aimed at voluntary vaccinators while avoiding overspending. Once this is achieved, it makes little difference whether the subsidy fully or partly offsets the vaccination cost.

The 1-dimensional discrete Voronoi game

The discrete Voronoi game in R consists of two competing players P1 and P2 and a set of N users placed on a line-segment. The players alternately place one facility each on the line-segment for R-rounds, where the objective is to maximize their own total payoffs. We prove bounds on the worst-case (over the arrangement of the N users) payoffs of the two players, and discuss algorithms for finding the optimal strategies of the players in the 2-round game.

Best experienced payoff dynamics and cooperation in the centipede game

We study population game dynamics under which each revising agent tests each of his strategies a fixed number of times, with each play of each strategy being against a newly drawn opponent, and chooses the strategy whose total payoff was highest. In the centipede game, thesebest experienced payoff dynamicslead to cooperative play. When strategies are tested once, play at the almost globally stable state is concentrated on the last few nodes of the game, with the proportions of agents playing each strategy being largely independent of the length of the game. Testing strategies many times leads to cyclical play.

Equity Concerns are Narrowly Framed

Distributional decisions regularly involve multiple payoff components. In a series of experiments involving over 3,300 subjects and 81,000 decisions, we find that—even when payoff components can be easily aggregated—many subjects exhibit narrow equity concerns, applying fairness preferences to a single component of payoffs. This behavior leads to preference reversals; subjects make different choices depending on which payoff component is used to denominate their decision. In our simplest setting, in which the two payoff components are small and large tokens, displaying narrow equity concerns is 63%–83% as prevalent as achieving equity in total payoffs and just as prevalent as applying the well-documented norm of a 50/50-split. Subjects also exhibit narrowly equity concerns over payoffs of time and money.

A Centralized Smart Decision-Making Hierarchical Interactive Architecture for Multiple Home Microgrids in Retail Electricity Market

The principal aim of this study is to devise a combined market operator and a distribution network operator structure for multiple home-microgrids (MH-MGs) connected to an upstream grid. Here, there are three distinct types of players with opposite intentions that can participate as a consumer and/or prosumer (as a buyer or seller) in the market. All players that are price makers can compete with each other to obtain much more possible profitability while consumers aim to minimize the market-clearing price. For modeling the interactions among partakers and implementing this comprehensive structure, a multi-objective function problem is solved by using a static, non-cooperative game theory. The propounded structure is a hierarchical bi-level controller, and its accomplishment in the optimal control of MH-MGs with distributed energy resources has been evaluated. The outcome of this algorithm provides the best and most suitable power allocation among different players in the market while satisfying each player’s goals. Furthermore, the amount of profit gained by each player is ascertained. Simulation results demonstrate 169% increase in the total payoff compared to the imperialist competition algorithm. This percentage proves the effectiveness, extensibility and flexibility of the presented approach in encouraging participants to join the market and boost their profits.

The effect of initial inequality on meritocracy: A voting experiment on tax redistribution

According to Alesina and Angeletos (2005), societies are less redistributive but more efficient when the median voter believes that effort and talent are much more important than luck in determining income. We test these results through a lab experiment in which participants vote over the tax rate and their pre-tax income is determined according to their performance in a real-effort task with leisure time. Subjects receive either a high or a low wage and this condition is either obtained through their talent in a tournament or randomly assigned. We compare subjects' decisions in these two different scenarios, taking into consideration different levels of wage inequality. In our framework, this initial income inequality turns out to be crucial to support the theoretical hypothesis of Alesina and Angeletos (2005). Overall, we find that, only if the wage inequality is high, subjects choose a lower level of income redistribution and provide a higher effort level in the scenario in which high-wage subjects are selected based on their talent through a tournament (than when it is randomly assigned). Thus, we confirm almost all theoretical results in Alesina and Angeletos (2005) when the wage inequality is high enough. The big exception is for efficiency (measured as the sum of total payoffs), since theoretical results are not significant for both wage inequality scenarios.

Evolution reinforces cooperation with the emergence of self-recognition mechanisms: An empirical study of strategies in the Moran process for the iterated prisoner's dilemma.

We present insights and empirical results from an extensive numerical study of the evolutionary dynamics of the iterated prisoner’s dilemma. Fixation probabilities for Moran processes are obtained for all pairs of 164 different strategies including classics such as TitForTat, zero determinant strategies, and many more sophisticated strategies. Players with long memories and sophisticated behaviours outperform many strategies that perform well in a two player setting. Moreover we introduce several strategies trained with evolutionary algorithms to excel at the Moran process. These strategies are excellent invaders and resistors of invasion and in some cases naturally evolve handshaking mechanisms to resist invasion. The best invaders were those trained to maximize total payoff while the best resistors invoke handshake mechanisms. This suggests that while maximizing individual payoff can lead to the evolution of cooperation through invasion, the relatively weak invasion resistance of payoff maximizing strategies are not as evolutionarily stable as strategies employing handshake mechanisms.

Cash versus opportunity costs and revenues in bilateral bargaining

We extend previous experimental research on the relevance of cash versus opportunity costs for decision making to a bilateral bargaining setting in which we consider not only cash and opportunity costs, but also cash and opportunity revenues. In the negotiation between a seller and a buyer, a seller’s additional cash cost (cash revenue) reduces (increases) the welfare from trade, i.e., the sum of the partners’ payoffs in case they agree to cooperate, whereas an opportunity cost (revenue) represents a foregone profit (loss) outside the cooperation which does not affect the welfare from trade, but only the gain from trade, i.e., the increase in total payoffs of the two bargaining partners relative to the payoffs they can realize without cooperation. We employ theories of mental accounting and loss aversion to derive hypotheses that contrast bargaining outcomes with a standard-theoretic benchmark prediction implying that the bargaining partners will equally split the gain from trade irrespective of whether the additional item is a cash or opportunity cost or revenue. We hypothesize that prices are less sensitive to the additional item and thus deviate more strongly from the benchmark prediction when the item is an opportunity instead of a cash cost or revenue, because an opportunity cost or revenue is outside, whereas a cash cost or revenue is inside the relationship. We further hypothesize that prices are less sensitive to the item and thus deviate more strongly from the benchmark prediction when the item is an opportunity cost instead of an opportunity revenue, because the opportunity cost is in the gain domain, whereas the opportunity revenue is in the loss domain. Our experimental results support the former, but not the latter prediction. We conclude that the effect of cash versus opportunity costs or revenues on decision making critically depends on the strategic context in which they occur.

Pricing and Revenue Sharing Between ISPs Under Content Sponsoring

As sponsored data with subsidized access cost gains popularity in industry, it is essential to understand its impact on the Internet service market. We investigate the interplay among Internet Service Providers (ISPs), Content Provider (CP) and End User (EU), where each player is selfish and wants to maximize its own profit. In particular, we consider multi-ISP scenarios, in which the network connectivity between the CP and the EU is jointly provided by multiple ISPs. We first model non-cooperative interaction between the players as a four-stage Stackelberg game, and derive the optimal behaviors of each player in equilibrium. Taking into account the transit price at intermediate ISP, we provide in-depth understanding on the sponsoring strategies of CP. We then study the effect of cooperation between the ISPs to the pricing structure and the traffic demand, and analyze their implications to the players. We further build our revenue sharing model based on Shapley value mechanism, and show that the collaboration of the ISPs can improve their total payoff with a higher social welfare.

Efficient computation of the Shapley value for large-scale linear production games

The linear production game is concerned with allocating the total payoff of an enterprise among the owners of the resources in a fair way. With cooperative game theory providing a mathematical framework for sharing the benefit of the cooperation, the Shapley value is one of the widely used solution concepts as a fair measurement in this area. Finding the exact Shapley value for linear production games is, however, challenging when the number of players exceeds 30. This paper describes the use of linear programming sensitivity analysis for a more efficient computation of the Shapley value. The paper also proposes a stratified sampling technique to estimate the Shapley value for large-scale linear production games. Computational results show the effectiveness of the proposed methods compared to others.