Reciprocity Game Research Articles

Cooperative Game Analysis based on Country Size and Market Position

This paper studies the cooperative game theory, and analyzes the cooperative game with international scale and market position. From the perspective of evolutionary game theory, this paper discusses the preconditions for big and small countries to participate in regional economic cooperation and the stability conditions of economic cooperation. This paper combines cooperative game theory with regional economic integration, and the economic and political alliance among countries can be regarded as a cooperative game. In order to analyze the cooperation of member countries, the countries are divided into small countries and big countries according to their size and market position, and the replication dynamic equation is calculated, then the basic conditions of the strategy of big countries and small countries participating in regional economic alliance are obtained, and the strategy selection probability of participants under the conditions of equilibrium strategy and non-equilibrium strategy is analyzed. In addition, using evolutionary game theory and Jacobian matrix to analyze the stability of local equilibrium point, a reciprocal game model of regional economic cooperation between big and small countries is established. Through the research, it is found that the necessary condition for the formation of regional economic integration is the economic complementarity among the cooperative parties, and the sufficient condition is that the cooperative parties can coordinate the distribution of interests among themselves through effective consultation and finally reach a binding agreement on the distribution of interests, thus restricting each other's economic behavior.

A Sequential Reciprocity Game Model of International Tourism Cooperation under the Background of “One Belt and One Road”

ABSTRACT Based on Dufwenberg and Kirchsteiger’s sequential reciprocity game model, this study aims to establish the sequential reciprocal game model based on international tourism cooperation and analyzes the game behavior between China and a certain country. The findings indicate that a certain country that is rational or does not have enough reciprocal motivation will adopt the noncooperative strategy when China adopts the noncooperative strategy. A certain country that has enough reciprocal motivation will adopt the cooperative strategy when China adopts the cooperative strategy. Moreover, a certain country will adopt the cooperative strategy with certain probability when their reciprocity motivation lies between the above two cases. The conclusions will provide a positive reference for countries tourism cooperation decision.

RPO-MAC: reciprocal Partially observable MAC protocol based on application-value-awareness in VANETs

Numerous safety-related applications have rigid requirements for the threshold of latency limitation of message transmissions to enhance safety and traffic efficiency of vehicles on the road in vehicular ad-hoc networks (VANETs). Consequently, a medium access control (MAC) protocol for reliable and fast transmission of safety messages should focus on the maximum transmission delay. Herein, we refer to the concept of packet value and integrate it with the latency of different messages determined by the waiting interval of packets in a queue. Subsequently, we propose a reciprocal revenue function, i.e., the transmission probability of the participants, by considering both its own benefit and the other nodes’ revenue. Additionally, an inter-vehicle cross-layer cooperative game model based on the local optimal utility of participants is constructed. We then theoretically prove the existence of an equilibrium using the partially observable Markov decision process (POMDP), and provide a specific approach for obtaining the channel access probability of a vehicle by using deep reinforcement learning. Finally, the analysis and simulation results in saturated and non-saturated data traffic conditions are presented to evaluate the performance of Reciprocal Partially Observable MAC Protocol (RPO-MAC) proposed in this paper and compare it with the IEEE 802.11p standard protocol. These comparisons demonstrate the advantages of our proposed reciprocal revenue game method in the case of channel network congestion, especially in terms of delay. It is shown that the RPO-MAC protocol can provide a strong support to delay-sensitive safety related applications.

A Note on Stabilizing Cooperation in the Centipede Game

In the much-studied Centipede Game, which resembles the Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even though continuing play can benefit both players—but not if the rival defects immediately, which it has an incentive to do. We show that, without changing the structure of the game, interchanging the payoffs of the two players provides each with an incentive to cooperate whenever its turn comes up. The Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, wherein there are several Nash equilibria. The Reciprocity Game can be implemented noncooperatively by adding, at the start of the Centipede Game, a move to exchange payoffs, which it is rational for the players to choose. What this interchange signifies, and its application to transforming an arms race into an arms-control treaty, are discussed.

Reciprocity Game

AbstractThis paper shows that reciprocity comes from the desire to cooperate in finitely repeated prisoner's dilemma game. Before playing the finitely repeated prisoner's dilemma game, players choose the reciprocity level and commit to it, and the reciprocity level is public information. There are T equilibria if the prisoner's dilemma game is repeated for T periods, and each equilibrium is associated with different levels of cooperation. Further, if players choose their reciprocity levels sequentially, then the most cooperative equilibrium will be the unique equilibrium. However, reciprocity does not matter for the one‐period game and the infinitely repeated game.

An Indirect-Reciprocity-Based Incentive Framework for Multimedia Service Through Device-to-Device Multicast

Instead of delivered directly by the base station (BS), in a device-to-device multicast (D2MD) system, the multimedia content is broadcasted to the request nodes (RNs) by the head node (HN) that has cached the content, and thus the system's performances can be greatly improved. However, the content delivery consumes energy. If the cost cannot get compensated from the cooperation, the HN may refuse to serve the RNs due to the selfish and rational nature. In such a case, how to stimulate the HN to cooperate is an essential issue. In this paper, we propose an indirect reciprocity game framework to investigate the D2MD stimulation problem, where the service level of the content and the location distribution of the RNs are taken into account. In the game, the HN will be assigned a reputation value after its delivery (i.e., action), based on which the HN can get some rewards in the future. Due to the channel fading gain, the HN's action and reputation value will be distorted. Taking such a distortion into consideration, we propose a reputation updating policy to update the HN's reputation, where the deviation of the HN's reputation is captured by the concept of reputation distributions. We prove theoretically that even under the influence of channel fading, there exists a stationary reputation distribution of the whole system. To find the optimal action rule of the HN in the game, we propose a modified value iteration algorithm. We prove that within an appropriate cost-to-gain ratio, the optimal action for the HN is to serve all the RNs. Such an optimal strategy is also proved to be an evolutionarily stable strategy (ESS) under the perturbation effect of the HN's action selection. The simulation results show that the proposed scheme is superior to the existing schemes in terms of portion of the served RNs, system throughput and energy efficiency.

Do good and talk about it! Disclosure and reward of discretionary kindness

Does it pay off for companies to disclose voluntary commitments to their customers? While voluntary commitments to enhance customers’ benefits became prevalent in many markets, systematic evidence on how customers (if at all) reward companies, which disclose such discretionary kindness, is still lacking. We analyze the consequences of endogenous disclosure of discretionary kindness in a novel experiment (N=636). We model the decision situation in a bilateral reciprocity game with asymmetric information on the vol-untariness of kindness. Experimental data show that endogenously disclosing discretionary kindness significantly triggers rewards from customers and does not backfire. Findings are robust towards variations in costs of information and the level of customers’ benefits. Survey evidence from a vignette study support our behavioral findings.

On the Transportability of Laboratory Results

The “transportability” of laboratory findings to other instances than the original implementation entails the robustness of rates of observed behaviors and estimated treatment effects to changes in the specific research setting and in the sample under study. In four studies based on incentivized games of fairness, trust, and reciprocity, we evaluate (1) the sensitivity of laboratory results to locally recruited student-subject pools, (2) the comparability of behavioral data collected online and, under varying anonymity conditions, in the laboratory, (3) the generalizability of student-based results to the broader population, and (4) with a replication at Amazon Mechanical Turk, the stability of laboratory results across research contexts. For the class of laboratory designs using incentivized games as measurement instruments of prosocial behavior, we find that rates of behavior and the exact behavioral differences between decision situations do not transport beyond specific implementations. Most clearly, data obtained from standard participant pools differ significantly from those from the broader population. This undermines the use of empirically motivated laboratory studies to establish descriptive parameters of human behavior. Directions of the behavioral differences between games, in contrast, are remarkably robust to changes in samples and settings. Moreover, we find no evidence for either anonymity effects nor mode effects potentially biasing laboratory measurement. These results underscore the capacity of laboratory experiments to establish generalizable causal effects in theory-driven designs.

The Evolution of Morals Under Indirect Reciprocity

We study the coexistence of strategies in the indirect reciprocity game where agents have access to second-order information. We fully characterize the evolutionary stable equilibria and analyze their comparative statics with respect to the cost-benefit ratio (CBR). There are indeed only two stable sets of equilibria enabling cooperation, one for low CBRs involving two strategies and one for higher CBR’s which involves two additional strategies. We thereby offer an explanation for the coexistence of different moral judgments among humans. Both equilibria require the presence of second-order discriminators which highlights the necessity for higher-order information to sustain cooperation through indirect reciprocity. In a laboratory experiment, we find that more than 75% of subjects play strategies that belong to the predicted equilibrium set. Furthermore, varying the CBR across treatments leads to changes in the distribution of strategies that are in line with theoretical predictions.

T213. THE EFFECT OF ACUTE STRESS ON PARANOID THINKING AND CORTISOL DURING SOCIAL INTERACTION IN HIGH AND LOW SCHIZOTYPES

BackgroundParanoid thinking, a common symptom of psychosis and schizophrenia, manifests as a sense of threat and may also be indexed by a lack of trust. Stress, in turn, exacerbates psychosis and paranoia, and is a well-established risk factor for schizophrenia as well as a component in several models of psychosis. The present study aimed to determine the impact that acute stress has on paranoid thinking during social interaction in vivo in high (HSZ) vs low (LSZ) schizotypy using an iterated social reciprocity game. The main hypothesis was that HSZ would anticipate grerater social threat and paranoia at baseline compared to LSZ, and moreover that experimentally-induced stress would exacerbate those differences, and thus show that stress differentially modulates how HSZ model the intentions of others.MethodsMatched healthy participants were stratified into HSZ (N=17) and LSZ (N=17) groups and were administered a non-financial, social-reciprocity game against benevolent and malevolent opponents under both stress and no-stress conditions. Stress was manipulated using the MIST (Dedovic et al., 2005) stress paradigm. Cortisol was measured from saliva samples acquired before and after the MIST stress task. Anticipation of threat and trust scores were derived from the social interaction task.ResultsAt baseline, cortisol levels were not significantly different between HSZ and LSZ but were significantly raised by the stressor task in HSZ (p<.05) but not in LSZ. Higher cortisol at baseline (pre-stress) predicted greater initial and average anticipation of threat (both r=.5, p<.05) (no-stress) to other players; and lower initial trust ratings of malevolent, but not benevolent, players. The MIST task significantly elevated stress ratings compared to baseline (p<.001) and following stress, greater change in cortisol from baseline to post-MIST was associated with lower trust ratings (r=.51, p<.05). In HSZ greater stressor-related cortisol levels correlated with greater anticipation of threat (r=.58, p<.05) and lower trust levels (r=.57, p<.05) which was not apparent in low schizotypes.DiscussionAcute stress elevates cortisol and paranoia in HSZ – in the form of greater anticipation of threat, and lower trust compared to LSZ. The study adds evidence to the role of stress in exacerbating schizophrenia-like experiences in those who are sub-threshold for schizophrenia and psychosis.

From the “squiggle game” to “games of reciprocity” towards a creative co-construction of a space for working with adolescents

ABSTRACTThe “squiggle game” is, above all, a method for relating and encouraging mutual exchange between the analyst and the patient (no matter if child, adolescent, or adult), enabling him to experience holding and freely explore different communication possibilities. After having explored the “technique” as it has been developed by Winnicott, this study also exposes some theoretical considerations, and some variations in the basic technique, brought together by the crucial role played by reciprocity: “Me a little and you a little.” The paper is a clinical case with a Chinese adolescent.

THE 'RECIPROCITY' GAME: A THEORETICAL BASIS FOR MEASURING RECIPROCITY IN HUMAN SOCIO-ECONOMIC INTERACTIONS

The Theory of Expected Utility is the central theory that describes the way individuals make a decision according to the classical economic theory. Despite the fact of that, experimental studies on individuals' behavioral attitude of the last 20 years have shown that this theory does not accurately represent human behavior from a descriptive point of view. On the contrary, these studies bear out that reciprocity is the motivational drive of human decisions. People have a reciprocal behavior if they praise and repay good deeds and punish unkind ones. On the other hand, they are rational if they make every effort to maximize the benefit and their utility. In this review paper, we present a theoretical framework of reciprocity's measuring through the experimental economics. In particular, we propose an experimental way of identifying the incentives under which the subjects make a decision. Are they motivated by other people's well-being or by material self-interest? For achieving this, Homo Economicus and Homo Reciprocans ''conflict'' amid two different games of Game Theory. These games (Ultimatum Game and Dictator Game) create a new one, which is called ''The Reciprocity Game'' and it is going to offer us an important theoretical basis for the empirical measurement of human reciprocity in the future.

Reciprocity Game

Reciprocity Game

Indirect-Reciprocity Data Fusion Game and Application to Cooperative Spectrum Sensing

Data sharing is one critical step to implement data fusion, and how to encourage sensors to share their data is an important issue. In this paper, we propose a reputation-based incentive framework, where the data sharing stimulation problem is modeled as an indirect reciprocity game. In the proposed game, sensors choose how to report their results to the fusion center and gain reputations, based on which they can obtain certain benefits in the future. Taking the sensing and fusion accuracy into account, reputation distribution is introduced in the proposed game, where we prove theoretically the Nash equilibrium of the game and its uniqueness. Furthermore, we apply the proposed scheme to the cooperative spectrum sensing. We show that within an appropriate cost-to-gain ration, the optimal strategy for the secondary users is to report when the average received energy is above a given threshold and keep silence otherwise. Such an optimal strategy is also proved to be a desirable evolutionarily stable strategy. Finally, simulation results are shown to verify the theoretical results and demonstrate that compared with the existing schemes, our proposed scheme achieves better operating characteristic curve and higher system throughput with convincing performance on fairness.

Multiple Criteria Relay Selection Scheme in Cooperative Communication Networks

This paper considers a wireless cooperative network with a base station (central unit) and many subscribers (users) in which the subscribers have the ability to relay information for each other to improve the overall network performance. In future wireless communication networks where subscribers are intellectual and pursue various objectives, they will not help relay information for others. This means that the viability of cooperative communication networks largely depends on the willingness of users to help. The reputation based schemes solved this problem by stimulating the users to cooperate with others. Besides, the average achievable rate at the destination node in a relay based network highly depends on the relay node location. Therefore, for a relay selection scheme, the choices of relay location, and the reputation of each user as well as signal-to-noise ratio, which is the main criterion for relay selection schemes, are important selection parameters. This paper proposes a novel multiple criteria relay selection scheme with a low implementation complexity. The proposed scheme incorporates reputation, SNR and location of the users in a highest-level design that not only selects the best relay node for each source-destination pair, but also assigns weight efficiently for each criterion. A simple and efficient optimization tool based on multiple criteria decision making method is employed to solve our formulated problem. In addition, a novel information theoretic measure, which effectively measures dissimilarity between candidate relay nodes and ideal solutions, is also investigated. Since the proposed scheme determines the potential relay nodes in order of their superiority based on the predetermined criteria, it can be utilized in multiple relay selection schemes in wireless relay networks and also in the indirect reciprocity game methods. Finally, the numerical results are provided to illustrate the comparisons between different typical experiments. To best of our knowledge, no prior work has studied the process of relay selection from this point of view.

The effect of reciprocity disposition on giving and repaying reciprocity behavior

Human beings have a general tendency for reciprocity in most societies. The internalized reciprocity norm assumption suggests that reciprocity disposition would encourage reciprocity towards strangers in one-shot interactions. To verify this, we examined the predictive ability of reciprocity dispositions for giving and repaying reciprocal behaviors. A sample of college students (N=98) participated in the reciprocity game in a laboratory, which comprised a prisoner dilemma game (PD) and dictator game (DG). The results indicated that reciprocity behavior occurred among strangers without face-to-face interactions. Reciprocity expectation predicted the choice of cooperation in the PD significantly. Positive and negative reciprocity dispositions had no effect on the strategy choice; however, they significantly predicted payoff allocation in the DG. Specifically, a higher positive reciprocity disposition led to more payoff allocation, while a higher negative reciprocity disposition led to less payoff allocation. In summary, strangers abide by the reciprocity norm, and the internalized reciprocity disposition exerts an influence on repaying behavior and accounts for some individual differences in reciprocity. These findings provide robust support for the internalized reciprocity norm assumption, and illustrate the process mechanism of human interaction among strangers. People may predict interpersonal interaction better through reciprocity dispositions and reciprocity valences.

Robustness of linkage strategy that leads to large-scale cooperation

One of the most well-known models to characterize cooperation among unrelated individuals is Social dilemma (SD). However there is no consensus about how to solve the SD by itself. Since SDs are often embedded in other social interactions, including indirect reciprocity games (IR), human can coordinate their behaviors across multiple games. Such coordination is called ‘linkage’. Recently linkage has been considered as a promising solution to resolve SDs, since excluding SD defectors (i.e. those who defected in SD) from indirectly reciprocal relationships functions as a costless sanction. A previous study performed mathematical modeling and revealed that a linkage strategy, which cooperates in SD and engages in the Standing strategy in IR based on the recipients' behaviors in both SD and IR, was an ESS against a non-linkage strategy which defects in SD and engages in the Standing strategy in IR based on recipients' behaviors only in IR (Panchanathan and Boyd, 2004). In order to investigate the robustness of the linkage strategy, we devised a non-linkage strategy, which cooperates in SD but does not link two games. First, we conducted a mathematical analysis and demonstrated that the linkage strategy was not an ESS against cooperating non-linkage strategy. Second, we conducted a series of agent-based computer simulations to examine how the strategies perform in situations in which various types of errors can occur. Our results showed that the linkage strategy was an ESS only when there are implementation errors in SD. However, the equilibrium of the linkage strategy was unstable when there are perception errors. Since we know that humans are not free from perception errors in their social life, future studies will need to show how perception errors can be overcome in order to provide support for the conclusion that linkage is a plausible solution to SDs.

Deception Undermines the Stability of Cooperation in Games of Indirect Reciprocity

Indirect reciprocity is often claimed as one of the key mechanisms of human cooperation. It works only if there is a reputational score keeping and each individual can inform with high probability which other individuals were good or bad in the previous round. Gossip is often proposed as a mechanism that can maintain such coherence of reputations in the face of errors of transmission. Random errors, however, are not the only source of uncertainty in such situations. The possibility of deceptive communication, where the signallers aim to misinform the receiver cannot be excluded. While there is plenty of evidence for deceptive communication in humans the possibility of deception is not yet incorporated into models of indirect reciprocity. Here we show that when deceptive strategies are allowed in the population it will cause the collapse of the coherence of reputations and thus in turn it results the collapse of cooperation. This collapse is independent of the norms and the cost and benefit values. It is due to the fact that there is no selection for honest communication in the framework of indirect reciprocity. It follows that indirect reciprocity can be only proposed plausibly as a mechanism of human cooperation if additional mechanisms are specified in the model that maintains honesty.

Transient nature of cooperation by pay-it-forward reciprocity.

Humans often forward kindness received from others to strangers, a phenomenon called the upstream or pay-it-forward indirect reciprocity. Some field observations and laboratory experiments found evidence of pay-it-forward reciprocity in which chains of cooperative acts persist in social dilemma situations. Theoretically, however, cooperation based on pay-it-forward reciprocity is not sustainable. We carried out laboratory experiments of a pay-it-forward indirect reciprocity game (i.e., chained gift-giving game) on a large scale in terms of group size and time. We found that cooperation consistent with pay-it-forward reciprocity occurred only in a first few decisions per participant and that cooperation originated from inherent pro-sociality of individuals. In contrast, the same groups of participants showed persisting chains of cooperation in a different indirect reciprocity game in which participants earned reputation by cooperating. Our experimental results suggest that pay-it-forward reciprocity is transient and disappears when a person makes decisions repeatedly, whereas the reputation-based reciprocity is stable in the same situation.

Incentive analysis for cooperative interactive multiview video streaming

In interactive multiview video streaming (IMVS), users can periodically select one out of many captured views available for observation. In single-view video streaming, cooperative strategies where peers share received packets of the same video have proven to be effective in reducing server׳s upload burden, and incentive mechanisms are designed to stimulate user cooperation. However, exploiting user cooperation in higher dimensional IMVS is difficult, since users watching different views makes it difficult to establish partnership, and users switching views frequently and independently makes it difficult to maintain partnership over time. In this paper, we use a multiview video frame structure for IMVS to support cooperative view-switching, where peers may help each other even if they are observing different views. We then model peers׳ interaction as an indirect reciprocity game, where each user is assigned a reputation level. To gain a higher reputation level, users help others, which in turn leads to a higher likelihood to receive others׳ help later. In this work, we focus on how view switching, the key feature of IMVS, affects user cooperation. By modeling users׳ decision making as a Markov decision process, our analysis shows that users tend to cooperate at some views but not others: given peers can predict their future view navigation paths probabilistically, for a peer who is likely to enter a view-switching path not requiring others׳ help, he also has less incentive to cooperate. Furthermore, we observe that the game may have multiple Nash Equilibria corresponding to different cooperation levels, e.g., users cooperate at all views in the full cooperation equilibrium, while users only cooperate at certain views in the partial cooperation equilibrium. The particular equilibrium the game will converge to depends on the initial cooperation level of the game. To stimulate user cooperation at all views, we propose a Pay-for-Cooperation (PfC) scheme at the beginning of the game to drive the game to the full cooperation equilibrium to improve system efficiency. Our simulation results show the effectiveness of PfC.