Games, Volume 11, Issue 4 (December 2020) – 25 articles

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models. Full article

In a two-period game, Player 1 produces zero-day exploits for immediate deployment or stockpiles for future deployment. In Period 2, Player 1 produces zero-day exploits for immediate deployment, supplemented by stockpiled zero-day exploits from Period 1. Player 2 defends in both periods. The article illuminates how players strike balances between how to exert efforts in the two periods, depending on asset valuations, asset growth, time discounting, and contest intensities, and when it is worthwhile for Player 1 to stockpile. Eighteen parameter values are altered to illustrate sensitivity. Player 1 stockpiles when its unit effort cost of developing zero-day capabilities is lower in Period 1 than in Period 2, in which case it may accept negative expected utility in Period 1 and when its zero-day appreciation factor of stockpiled zero-day exploits from Period 1 to Period 2 increases above one. When the contest intensity in Period 2 increases, the players compete more fiercely with each other in both periods, but the players only compete more fiercely in Period 1 if the contest intensity in Period 1 increases. Full article

In this paper, we study the structure of trajectories of discrete disperse dynamical systems with a Lyapunov function which are generated by set-valued mappings. We establish a weak version of the turnpike property which holds for all trajectories of such dynamical systems which are of a sufficient length. This result is usually true for models of economic growth which are prototypes of our dynamical systems. Full article

This paper focuses on the design and analysis of short-term control intervention measures seeking to suppress local populations of Aedes aegypti mosquitoes, the major transmitters of dengue and other vector-borne infections. Besides traditional measures involving the spraying of larvicides and/or insecticides, we include biological control based on the deliberate introduction of predacious species feeding on the aquatic stages of mosquitoes. From the methodological standpoint, our study relies on application of the optimal control modeling framework in combination with the cost-effectiveness analysis. This approach not only enables the design of optimal strategies for external control intervention but also allows for assessment of their performance in terms of the cost-benefit relationship. By examining numerous scenarios derived from combinations of chemical and biological control measures, we try to find out whether the presence of predacious species at the mosquito breeding sites may (partially) replace the common practices of larvicide/insecticide spraying and thus reduce their negative impact on non-target organisms. As a result, we identify two strategies exhibiting the best metrics of cost-effectiveness and provide some useful insights for their possible implementation in practical settings. Full article

We experimentally compare the consequences for group cooperation of two decision mechanisms involving the extension of group membership. We analyze an exogenous decision (random draw) and an endogenous decision (made by a particular group member) mechanism to extend a temporary agent’s group membership. Our results reveal that the prospect of group membership extension affects not only the temporary but also the permanent group members’ contributions with an endogenous mechanism. Full article

We formulate and study a nonlinear game of n symmetric countries that produce, pollute, and spend part of their revenue on pollution mitigation and environmental adaptation. The optimal emission, adaptation, and mitigation investments are analyzed in both Nash equilibrium and cooperative cases. Modeling assumptions and outcomes are compared to other publications in this fast-developing area of environmental economics. In particular, our analysis implies that: (a) mitigation is more effective than adaptation in a crowded multi-country world; (b) mitigation increases the effectiveness of adaptation; (c) the optimal ratio between mitigation and adaptation investments in the competitive case is larger for more productive countries and is smaller when more countries are involved in the game. Full article

Wage rates, efficiency wages, and gift exchange in a labor market are all crucial aspects in regard to designing contracts to ensure high effort from workers. We extend this literature by discussing the relationship between known differences in wages (social comparison) and workers’ effort provision. We conduct an experiment in which subjects perform effort tasks for piece-rates. All subjects are paid the same wage rate in the first half of the experiment, but in the second half are paid different wage rates; the primary variable we study is the information about others’ wage rates given to a subset of subjects. We find that subjects’ efforts respond strongly to information about others’ wages. Such findings have implications for contract structuring for workers. Full article

“Image scoring” is a type of social evaluation, originally used in agent-based models, where the reputation of another is numerically assessed. This phenomenon has been studied in both theoretical models and real-life psychology experiments (using human participants). The latter are aimed to create conditions in the laboratory where image scoring can be elicited. One influential paper is that of Wedekind and Milinski (2000), WM. Our paper is a replication of that study, deliberately employing very similar methodology to the original. Accordingly, we had six groups of ten participants play an economic game. In each round, each player was randomly paired with another player whose identity was unknown. The participant was given a binary choice of either (1) donating money to that person, or (2) not donating money. In each round, the player was passively exposed to information about the past generosity of the other player. In our study, we successfully replicated the central result of WM. Participants in our replication gave significantly more money to partners with higher image scores (more generous reputations) than those with lower image scores (less generous reputations). This paper also provides a critical review of the methodology of WM and the study of image scoring. Full article

The confirmation bias, unlike other decision biases, has been shown both empirically and in theory to be enhanced with deliberation. This suggests that limited attention, reduced deliberation, or limited available cognitive resources may moderate this bias. We aimed to test this hypothesis using a validated confirmation bias task in conjunction with a protocol that randomly assigned individuals to one week of at-home sleep restriction (SR) or well-rested (WR) sleep levels. We also used a measure of cognitive reflection as an additional proxy for deliberation in our analysis. We tested the hypotheses that the confirmation bias would be stronger for WR participants and those higher in cognitive reflection on a sample of 197 young adults. Our results replicated previous findings, and both males and females separately displayed the confirmation bias. Regarding our deliberation hypotheses, the confirmation bias results were most precisely estimated for those having thought relatively more about the issue of gun control. Additionally, for the subset of individuals having thought relatively more about gun control, we found evidence that the confirmation bias was stronger for those higher in cognitive reflection and, somewhat less robustly, for those participants who were (objectively) well-rested. Full article

We derive an extremum principle. It can be treated as an intermediate result between the celebrated smooth-convex extremum principle due to Ioffe and Tikhomirov and the Dubovitskii–Milyutin theorem. The proof of this principle is based on a simple generalization of the Fermat’s theorem, the smooth-convex extremum principle and the local implicit function theorem. An integro-differential example illustrating the new principle is presented. Full article

The coalition literature has thrived during the 20th century, and now constitutes not only a consolidated field in political science, but also one of the most productive fields in terms of theoretical and methodological approaches. Throughout this history, coalition models have played a key role in tailoring explanations about various phenomena such as coalition formation, functioning, and breakdown. Nonetheless, a serious appreciation of their contribution to the development of the field is still lacking. In this context, this paper proposes a taxonomy of models that aims to assess the various functions that coalition models are designed for. I argue that models come in different flavours, namely: conceptual, whose goal consists in formalising abstract concepts via mathematical expressions; quasi-conceptual, which aim to explain empirical regularities; and extrapolative, which test hypotheses with empirical data. The paper surveys classical and more recent works, drawing attention to the different types of models, as well as their theoretical and empirical contributions to the coalition literature. Full article

Pursuit-evasion games are used to define guidance strategies for multi-agent planning problems. Although optimal strategies exist for deterministic scenarios, in the case when information about the opponent players is imperfect, it is important to evaluate the effect of uncertainties on the estimated variables. This paper proposes a method to characterize the game space of a pursuit-evasion game under a stochastic perspective. The Mahalanobis distance is used as a metric to determine the levels of confidence in the estimation of the Zero Effort Miss across the capture zone. This information can be used to gain an insight into the guidance strategy. A simulation is carried out to provide numerical results. Full article

CAR T-cell immunotherapy is a new development in the treatment of leukemia, promising a new era in oncology. Although so far, this procedure only helps 50–90% of patients and, like other cancer treatments, has serious side effects. In this work, we have proposed a controlled model for leukemia treatment to explore possible ways to improve immunotherapy methodology. Our model is described by four nonlinear differential equations with two bounded controls, which are responsible for the rate of injection of chimeric cells, as well as for the dosage of the drug that suppresses the so-called “cytokine storm”. The optimal control problem of minimizing the cancer cells and the activity of the cytokine is stated and solved using the Pontryagin maximum principle. The five possible optimal control scenarios are predicted analytically using investigation of the behavior of the switching functions. The optimal solutions, obtained numerically using BOCOP-2.2.0, confirmed our analytical findings. Interesting results, explaining, why therapies with rest intervals (for example, stopping injections in the middle of the treatment interval) are more effective (within the model), rather than with continuous injections, are presented. Possible improvements to the mathematical model and method of immunotherapy are discussed. Full article

In this paper, we develop a new dynamic model of optimal investments in R&D and manufacturing for a technological leader competing with a large number of identical followers on the market of a technological product. The model is formulated in the form of the infinite time horizon stochastic optimization problem. The evolution of new generations of the product is treated as a Poisson-type cyclic stochastic process. The technology spillovers effect acts as a driving force of technological change. We show that the original probabilistic problem that the leader is faced with can be reduced to a deterministic one. This result makes it possible to perform analytical studies and numerical calculations. Numerical simulations and economic interpretations are presented as well. Full article

In this article, a class of mean-field-type games with discrete-continuous state spaces is considered. We establish Bellman systems which provide sufficiency conditions for mean-field-type equilibria in state-and-mean-field-type feedback form. We then derive unnormalized master adjoint systems (MASS). The methodology is shown to be flexible enough to capture multi-class interaction in epidemic propagation in which multiple authorities are risk-aware atomic decision-makers and individuals are risk-aware non-atomic decision-makers. Based on MASS, we present a data-driven modelling and analytics for mitigating Coronavirus Disease 2019 (COVID-19). The model integrates untested cases, age-structure, decision-making, gender, pre-existing health conditions, location, testing capacity, hospital capacity, and a mobility map of local areas, including in-cities, inter-cities, and internationally. It is shown that the data-driven model can capture most of the reported data on COVID-19 on confirmed cases, deaths, recovered, number of testing and number of active cases in 66+ countries. The model also reports non-Gaussian and non-exponential properties in 15+ countries. Full article

We consider the dynamic network formation problem under the requirement that the whole network be connected and remain connected after q nodes are destroyed. We propose the concept of dynamic ${\mathcal{C}}^q$-stability and characterize dynamic ${\mathcal{C}}^q$-stable networks for any $q\ge 0$. Comparison with the outcome in the static model is also discussed. Full article

We studied how communication media affect trust game play. Three popular media were considered: traditional face-to-face, Facebook groups, and anonymous online chat. We considered post-communication changes in players’ expectations and preferences, and further analyzed the contents of group communications to understand the channels though which communication appears to improve trust and trustworthiness. For senders, the social, emotional, and game-relevant contents of communication all matter, significantly influencing both their expectations of fair return and preferences towards receivers. Receivers increased trustworthiness is mostly explained by their adherence to the norm of sending back a fair share of the amount received. These results do not qualitatively differ among the three communication media; while face-to-face had the largest volume of messages, all three media proved equally effective in enhancing trust and trustworthiness. Full article

Games are particularly relevant for field research in agriculture, where alternative experimental designs can be costly and unfeasible. Games are also popular for non-experimental purposes such as recreating learning experiences and facilitating dialogue with local communities. After a systematic review of the literature, we found that the volume of published studies employing coordination and cooperation games increased during the 2000–2020 period. In recent years, more attention has been given to the areas of natural resource management, conservation, and ecology, particularly in regions important to agricultural sustainability. Other games, such as trust and risk games, have come to be regarded as standards of artefactual and framed field experiments in agriculture. Regardless of their scope, most games’ results are subject to criticism for their internal and external validity. In particular, a significant portion of the games reviewed here reveal recruitment biases towards women and provide few opportunities for continued impact assessment. However, games’ validity should be judged on a case-by-case basis. Specific cultural aspects of games might reflect the real context, and generalizing games’ conclusions to different settings is often constrained by cost and utility. Overall, games in agriculture could benefit from more significant, frequent, and inclusive experiments and data—all possibilities offered by digital technology. Present-day physical distance restrictions may accelerate this shift. New technologies and engaging mediums to approach farmers might present a turning point for integrating experimental and non-experimental games for agriculture in the 21st century. Full article

This paper studies the evolution of overconfidence over a cohort’s working life. To do this, the paper incorporates subjective assessments into a continuous time human capital accumulation model with a finite horizon. The main finding is that the processes of human capital accumulation, skill depreciation, and subjective assessments imply that overconfidence first increases and then decreases over the cohort’s working life. In the absence of skill depreciation, overconfidence monotonically increases over the cohort’s working life. The model generates four additional testable predictions. First, everything else equal, overconfidence peaks earlier in activities where skill depreciation is higher. Second, overconfidence is lower in activities where the distribution of income is more dispersed. Third, for a minority of individuals, overconfidence decreases over their working life. Fourth, overconfidence is lower with a higher market discount rate. The paper provides two applications of the model. It shows the model can help make sense of field data on overconfidence, experience, and trading activity in financial markets. The model can also explain experimental data on the evolution of overconfidence among poker and chess players. Full article

This paper uses the framework of stochastic games to propose a model of emotions in repeated interactions. An emotional player can be in either a friendly, a neutral, or a hostile state of mind. The player transitions between the states of mind as a response to observed actions taken by the other player. The state of mind determines the player’s psychological payoff which together with a material payoff constitutes the player’s utility. In the friendly (hostile) state of mind the player has a positive (negative) concern for other players’ material payoffs. This paper shows how emotions can both facilitate and obstruct cooperation in a repeated prisoners’ dilemma game. In finitely repeated games a player who cares only for their own material payoffs can have an incentive to manipulate an emotional player into the friendly state of mind. In infinitely repeated games with two emotional players less patience is required to sustain cooperation. However, emotions can also obstruct cooperation if they make the players unwilling to punish each other, or if the players become hostile when punished. Full article

We analyze the impact of overconfidence on the timing of entry in markets, profits, and welfare using an extension of the quantity commitment game. Players have private information about costs, one player is overconfident, and the other one rational. We find that for slight levels of overconfidence and intermediate cost asymmetries, there is a unique cost-dependent equilibrium where the overconfident player has a higher ex-ante probability of being the Stackelberg leader. Overconfidence lowers the profit of the rational player but can increase that of the overconfident player. Consumer rents increase with overconfidence while producer rents decrease which leads to an ambiguous welfare effect. Full article

This article focuses on the strategic behavior of firms in the output and the emissions markets in the presence of market power. We consider the existence of a dominant firm in the permit market and different structures in the output market, including Cournot and two versions of the Stackelberg model, depending on whether the permit dominant firm is a leader or a follower in the output market. In all three models, the firm that dominates the permit market is more sensitive to its initial allocation than its competitor in terms of abatement and less sensitive in terms of output. In all three models, output is decreasing and the permit price is increasing in the permit dominant firm’s initial allocation. In the Cournot model, permit dominance is fruitless in terms of output and profit if the initial allocation is symmetric. Output leadership is more relevant than permit dominance since an output leader always tends to, ceteris paribus, produce more and make more profit whether it also dominates the permit market or not. This leadership can only be overcompensated for by distributing a larger share of permits to the output follower, and only if the total number of permits is large enough. In terms of welfare, Stackelberg is always superior to Cournot. If the initial permit allocation is symmetric, welfare is higher when the same firm dominates the output and the permit market at the same time. Full article

To avoid the dangerous consequences of climate change, humans need to overcome two intertwined conflicts. First, they must deal with an intra-generational conflict that emerges from the allocation of costs of climate change mitigation among different actors of the current generation. Second, they face an inter-generational conflict that stems from the higher costs for long-term mitigation measures, particularly helping future generations, compared to the short-term actions aimed at adapting to the immediate effects of climate change, benefiting mostly the current generation. We devise a novel game to study this multi-level conflict and investigate individuals’ behavior in a lab experiment. We find that, although individuals reach sufficient cooperation levels to avoid adverse consequences for their own generation, they contribute more to cheaper short-term than to costlier long-term measures, to the detriment of future generations. Simple “nudge” interventions, however, may alter this pattern considerably. We find that changing the default contribution level to the inter-generational welfare optimum increases long-term contributions. Moreover, providing individuals with the possibility to commit themselves to inter-generational solidarity leads to an even stronger increase in long-term contributions. Nevertheless, the results also suggest that nudges alone may not be enough to induce inter-generationally optimal contributions. Full article

Cooperation in social dilemmas plays a pivotal role in the formation of systems at all levels of complexity, from replicating molecules to multi-cellular organisms to human and animal societies. In spite of its ubiquity, the origin and stability of cooperation pose an evolutionary conundrum, since cooperation, though beneficial to others, is costly to the individual cooperator. Thus natural selection would be expected to favor selfish behavior in which individuals reap the benefits of cooperation without bearing the costs of cooperating themselves. Many proximate mechanisms have been proposed to account for the origin and maintenance of cooperation, including kin selection, direct reciprocity, indirect reciprocity, and evolution in structured populations. Despite the apparent diversity of these approaches they all share a unified underlying logic: namely, each mechanism results in assortative interactions in which individuals using the same strategy interact with a higher probability than they would at random. Here we study the evolution of cooperation in both discrete strategy and continuous strategy social dilemmas with assortative interactions. For the sake of tractability, assortativity is modeled by an individual interacting with another of the same type with probability r and interacting with a random individual in the population with probability $1-r$, where r is a parameter that characterizes the degree of assortativity in the system. For discrete strategy social dilemmas we use both a generalization of replicator dynamics and individual-based simulations to elucidate the donation, snowdrift, and sculling games with assortative interactions, and determine the analogs of Hamilton’s rule, which govern the evolution of cooperation in these games. For continuous strategy social dilemmas we employ both a generalization of deterministic adaptive dynamics and individual-based simulations to study the donation, snowdrift, and tragedy of the commons games, and determine the effect of assortativity on the emergence and stability of cooperation. Full article