Games, Volume 13, Issue 1 (February 2022) – 19 articles

Multi-player mean-payoff games are a natural formalism for modelling the behaviour of concurrent and multi-agent systems with self-interested players. Players in such a game traverse a graph, while attempting to maximise a (mean-)payoff function that depends on the play generated. As with all games, the equilibria that could arise may have undesirable properties. However, as system designers, we typically wish to ensure that equilibria in such systems correspond to desirable system behaviours, for example, satisfying certain safety or liveness properties. One natural way to do this would be to specify such desirable properties using temporal logic. Unfortunately, the use of temporal logic specifications causes game theoretic verification problems to have very high computational complexity. To address this issue, we consider $\omega$-regular specifications. These offer a concise and intuitive way of specifying system behaviours with a comparatively low computational overhead. The main results of this work are characterisation and complexity bounds for the problem of determining if there are equilibria that satisfy a given $\omega$-regular specification in a multi-player mean-payoff game in a number of computationally relevant game-theoretic settings. Full article

Debates on an EU-leaving referendum arose in several member states after Brexit. We want to highlight how the exit of an additional country affects the power distribution in the Council of the European Union. We inspect the power indices of the member states both with and without the country which might leave the union. Our results show a pattern connected to a change in the number of states required to meet the 55% threshold. An exit that modifies this number benefits the countries with high population, while an exit that does not cause such a change benefits the small member states. According to our calculations, only the exit of Poland would be supported by the qualified majority of the Council. Full article

Given a fixed network that links various actors, we introduce a formal model that describes the structural stability of coalitions. To this end, we used the partition of the set of all actors in three distinct positions: members, i.e., those who are central to a coalition; participants, i.e., those who are not actively engaged with the issues at hand; neutral actors, i.e., non-members, those who are not party to any interests and outside the coalition. Using the language of networks, we formulated three assumptions that may be used to characterize the stability of this partition. We paid particular attention to the role of participants as they facilitate or complicate extensions of a given coalition. Given the fixed network, we (1) illustrate the verification of the stability of a coalition, (2) provide existence results of stable coalitions, and (3) set the limits to their credible extensions. Our three formal assumptions may serve as a platform for discussions regarding the stability of coalitions. Full article

In this study, we enrich a standard principal–agent model with hidden action by introducing salience-biased perception on the agent’s side. The agent’s misguided focus on salient payoffs, which leads the agent’s and the principal’s probability assessments to diverge, has two effects: First, the agent focuses too much on obtaining a bonus, which facilitates incentive provision. Second, the principal may exploit the diverging probability assessments to relax participation. We show that salience bias can reverse the nature of the inefficiency arising from moral hazard; i.e., the principal does not necessarily provide insufficient incentives that result in inefficiently low effort but instead may well provide excessive incentives that result in inefficiently high effort. Full article

We investigate experimentally whether players deliberately use irrelevant market cues to shape their evaluations of a traded item. We implement a repeated Vickrey median price selling auction of an unusual bad where players are informed on the market price and on the three lowest or highest asks. We elicited players’ consideration of market signals through a questionnaire at the end of the auction. We find that extreme information has a stronger influence on players’ evaluations than the market price. However, players’ consideration of the market signals explains their behavioral reactivity to the market price but not to the extremes. Hence, players deliberately use an unbiased estimator of the central tendency of the appraisals distribution, while extreme asks’ influence is consistent with a priming effect. Full article

We present a novel characterization of random rank-dependent expected utility for finite datasets and finite prizes. As a byproduct, we obtain a characterization of random expected utility that works for finite datasets. The test lends itself to statistical testing. We apply our test to an experimental dataset and find evidence against random expected utility, while random rank-dependent expected utility can explain the dataset. Full article

Take the fort, then take the city. In a two-stage, two-party contest, victory in the initial stage can provide an advantage in the final stage. We examine such momentum in conflict scenarios and investigate how valuable it must be to avoid a Pyrrhic victory. Our main finding is that although the elasticity of effort—which we allow to vary between the two stages—does impact the contestants’ effort levels, it has no bearing on the endogenously determined value of momentum itself. Further, rent dissipation in the two-stage conflict is equal across party whether or not an individual obtains first-stage momentum. Thus, momentum helps a player solely by enhancing marginal ability for victory in the second-stage contest. It does not, however, change the player’s net calculus of second-stage contest spending. Such contestable advantage is also found to be more rent-dissipative than innate/uncontestable advantage. Therefore, Pyrrhic victories should be more common for contests with an intermediate stage or stages in which advantages can be earned, ceteris paribus. While intermediate targets appear as useful conflict benchmarks, they dissipate additional expected contest rents. This additional rent-dissipative toll exists even for backward-inductive equilibrium behavior in a complete information setting. Whereas the quagmire theory suggests parties can become involved in problematic conflicts due to incomplete information, the present paper finds that the setting of conflict—namely, contestable intermediate advantage—can alternatively generate rent-dissipative tolls. Similarly, contestable advantage can lead parties to optimally forego contest participation (i.e., if conflict parameters do not meet the participation constraint). This is in contrast to a one-stage simultaneous contest with second-stage parametric values of the present contest. Full article

In many bargaining situations, the distribution of seats or voting weights does not accurately reflect bargaining power. Maaser, Paetzel and Traub (Games and Economic Behavior, 2019) conducted an experiment to investigate the effect of such nominal power differences in the classic Baron–Ferejohn model. This paper re-analyzes the data from that experiment, looking at gender differences in bargaining behavior and in the effect of nominal weights. We find that women and men differ in particular with respect to the proposed distribution of payoffs and coalition size. By contrast, nominal weights have only minor gender-specific effects. Full article

The effectiveness of control measures against the diffusion of the COVID-19 pandemic is grounded on the assumption that people are prepared and disposed to cooperate. From a strategic decision point of view, cooperation is the unreachable strategy of the Prisoner’s Dilemma game, where the temptation to exploit the others and the fear of being betrayed by them drives the people’s behavior, which eventually results in a fully defective outcome. In this work, we integrate a standard epidemic model with the replicator equation of evolutionary games in order to study the interplay between the infection spreading and the propensity of people to be cooperative under the pressure of the epidemic. The developed model shows high performance in fitting real measurements of infected, recovered and dead people during the whole period of COVID-19 epidemic spread, from March 2020 to September 2021 in Italy. The estimated parameters related to cooperation result to be significantly correlated with vaccination and screening data, thus validating the model. The stability analysis of the multiple steady states present in the proposed model highlights the possibility to tune fundamental control parameters to dramatically reduce the number of potential dead people with respect to the non-controlled case. Full article

In this article, we consider technology leaders (which are innovators) and technology followers (which are non-innovators) to provide a new theoretical explanation for the well-cited empirical evidence of an inverted-U relationship between competition and aggregate innovation. We consider a two-stage game with a deterministic Research and Development (R&D) process, where the leaders first determine their R&D investments simultaneously and then all leaders and followers determine their outputs simultaneously. We show that the inverted-U relationship between competition and aggregate innovation occurs if competition is affected by the number of technology followers. However, the presence of more technology leaders decreases individual R&D investments while increasing aggregate R&D investments. If the total number of firms remains the same but the composition of technology leaders and followers changes in favor of leaders (followers), individual R&D investments decrease (increase) but aggregate R&D investments increase (decrease). The relationship between competition and R&D investments can be U-shaped if the intensity of competition is measured by product substitutability. Contrary to the standard expectation, the presence of more firms may reduce welfare. Full article

White Lists are lists of firms set up at each Italian prefecture. It is a relatively young instrument born as an experimental project designed to solve problems for particular conditions of crime and corruption in the Italian territory. This work aims to understand if the “White List” tool can represent a reliable legality tool for the contracting station and representation for firms registered in these lists, an incentive to obtain awards for faster times of public procurement. Through a descriptive survey, we will try to photograph the “White List” phenomenon by comparing firms belonging to these lists with companies not belonging to them but which are similar in terms of size and economic sector. The comparison takes off some differences in the financial structure of the two groups of companies. in particular, the White List’s firms show a better profitability and a lower recourse to third-party capital. Full article

There has been much theoretical work aimed at understanding the evolution of social learning; and in most of it, individual and social learning are treated as distinct processes. A number of authors have argued that this approach is faulty because the same psychological mechanisms underpin social and individual learning. In previous work, we analyzed a simple model in which both individual and social learning are the result of a single learning process. Here, we extend this approach by showing how payoff and content biases evolve. We show that payoff bias leads to higher average fitness when environments are noisy and change rapidly. Content bias always evolves when the expected fitness benefits of alternative traits differ. Full article

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements. Full article

This paper presents a simple adaptive model of demand adjustment in cooperative games and analyzes this model in weighted majority games. In the model, a randomly chosen player sets her demand to the highest possible value subject to the demands of other coalition members being satisfied. This basic process converges to the aspiration set. By introducing some perturbations into the process, we show that the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, is the one most resistant to mutations. We then apply the process to weighted majority games. We show that in symmetric majority games and in apex games, the unique separating aspiration is the unique stochastically stable one. Full article

Free riding incentives make it difficult to control climate change. To improve the chances of the Paris Agreement’s ambitious goal, many nations are forming scientific networks in carbon capture and storage (CCS). These networks take many forms (bilateral, hub-and-spoke, and multilateral). Studies of social interactions among scientists demonstrate that research networks are limited because of relational issues, such as lack of trust. This paper provides a rationale for the formation of various types of international CCS networks and examines their impacts on climate change. Our concept of stability focuses on Nash equilibria that are immune to coalitional deviations in overlapping networks. Players may belong to various research networks. A particular research network is a climate club. We show that in the absence of top-down coordination in clubs, the type of global network that forms depends on relational attrition. The complex task is to mitigate free riding while enhancing trust. Full article

This study investigates the effect on nonprofessional investors’ judgements and decisions of discretionary measurement choices. Using a paper-and-pencil experience, we collect and analyze information regarding investment amounts as well as past and future financial performance judgements of firms’ earnings by manipulating fair value (mark-to-market and mark-to-model) criteria and benchmarking it with historical cost-based financial statements. We proxy nonprofessional investors with graduate students from a business school. Our results show evidence that nonprofessional investors view fair value changes as permanent. We argue for a cashflow volatility factor. Contrary to previous research, we do not find evidence of any effect on investors’ willingness to invest (average budget amounts invested) or performance judgments (past and future). We corroborate previous evidence that investors rank measurement concepts’ relevance differently for different classes, although, on average, mark-to-market fair values and historical cost are rated more relevant and reliable than mark-to-model fair values. Full article

We introduce a non-cooperative game model in which players’ decision nodes are partially ordered by a dependence relation, which directly captures informational dependencies in the game. In saying that a decision node v is dependent on decision nodes $v_1,\dots ,v_k$, we mean that the information available to a strategy making a choice at v is precisely the choices that were made at $v_1,\dots ,v_k$. Although partial order games are no more expressive than extensive form games of imperfect information (we show that any partial order game can be reduced to a strategically equivalent extensive form game of imperfect information, though possibly at the cost of an exponential blowup in the size of the game), they provide a more natural and compact representation for many strategic settings of interest. After introducing the game model, we investigate the relationship to extensive form games of imperfect information, the problem of computing Nash equilibria, and conditions that enable backwards induction in this new model. Full article

Motivated by recent examples of collective effort on the war on terror, we examine the incentives that retaliation may produce for the endogenous formation of an international counterterror coalition. We show that there are quite reasonable circumstances under which any nation that is a target of a terrorist attack finds it desirable to be a member of the international counterterror coalition, holding the choices of all other nations as given. The incentives to join the coalition are the group-specific benefits from retaliation enjoyed by each coalition member, the relatively lower spillover benefit from retaliation enjoyed by each stand-alone nation, and the inability of pre-emptive measures to avert terrorist attacks. The disincentive to join is the anticipated backlash from retaliation, which targets coalition members only. Full article