The game theory applied to the Covid-19 pandemic

The classification of COVID-19 as a pandemic by the World Health Organization (WHO), substantiated a global crisis in public and economic health, exposing failures of governments and markets in terms of the ability to act in a corrective, preventive and, above all, predictive manner, given the appearance of exogenous factors. One of the visible consequences of the pandemic is the polarization between Economy and Health in the countries, creating a competitive environment that resembles a duopoly where each player ends up acting and making their decisions according to what the other does. This article considers this scenario by quantitatively evaluating economic results that are possible to be achieved when in a negotiation essay between ‘Economics’ and ‘Health’, using the economic theory of games. The discussion developed points out to the existence of an “optimal strategy” for both the ‘Economy’ and ‘Health’ player, capable of maximizing the expected payoff for the population. From the application of the Pareto Equilibrium combined with the Coase Theorem, there is an opportunity to eliminate market and government failures with the achievement of a ‘Social Optimum’ throughout this and eventual future pandemics.

Bilateral costly expulsions resolve the public goods dilemma

Expulsion has been found to promote cooperation in social dilemmas, but only if it does not incur costs or is applied unilaterally. Here, we show that removing both conditions leads to a spontaneous resolution of the costly expulsion problem. Namely, by studying the public goods game where cooperators and defectors can expel others at a personal cost, we find that public cooperation thrives as expulsion costs increase. This is counterintuitive, as the cost of other-regarding behaviour typically places an additional burden on cooperation, which is in itself costly. Such scenarios are referred to as second-order free-rider problems, and they typically require an additional mechanism, such as network reciprocity, to be resolved. We perform a mean field analysis of the public goods game with bilateral costly expulsion, showing analytically that the expected payoff difference between cooperators and defectors increases with expulsion costs as long as players with the same strategy have, on average, a higher frequency to interact with each other. As the latter condition is often satisfied in social networks, our results thus reveal a fascinating new path to public cooperation, and they show that the costs of well-intended actions need not be low for them to be effective.

The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism

Background In recent years, the average abundance function has attracted much attention as it reflects the degree of cooperation in the population. Then it is significant to analyse how average abundance functions can be increased to promote the proliferation of cooperative behaviour. However, further theoretical analysis for average abundance function with mutation under redistribution mechanism is still lacking. Furthermore, the theoretical basis for the corresponding numerical simulation is not sufficiently understood. Results We have deduced the approximate expressions of average abundance function with mutation under redistribution mechanism on the basis of different levels of selection intensity $$\omega$$ ω (sufficiently small and large enough). In addition, we have analysed the influence of the size of group d, multiplication factor r, cost c, aspiration level $$\alpha$$ α on average abundance function from both quantitative and qualitative aspects. Conclusions (1) The approximate expression will become the linear equation related to selection intensity when $$\omega$$ ω is sufficiently small. (2) On one hand, approximation expression when $$\omega$$ ω is large enough is not available when r is small and m is large. On the other hand, this approximation expression will become more reliable when $$\omega$$ ω is larger. (3) On the basis of the expected payoff function $$\pi \left( \centerdot \right)$$ π ⋅ and function $$h(i,\omega )$$ h ( i , ω ) , the corresponding results for the effects of parameters (d,r,c,$$\alpha$$ α ) on average abundance function $$X_{A}(\omega )$$ X A ( ω ) have been explained.

Strategic voting revisited: the case of the 2018 Taipei City mayoral election

In this study, we examine whether strategic voting – in which a voter seeks to maximize the expected payoff from casting a ballot – occurred among late voters in the 2018 Taipei City mayoral election. This multi-candidate mayoral contest was noteworthy because ballot-counting started before all the votes had been cast, with preliminary results being leaked to the media. Theoretically, having access to real-time updates of voting figures could have influenced the decision of voters who were still in line waiting to cast their ballots. Analysis and reconstruction of aggregate polling data, however, demonstrate that there was very little (if any) strategic voting among these late voters on election day, even if they had information that might have induced them to vote strategically.

Decision process and preferences over risk under the “endogenous decision rule”: results from a group experiment

Recent literature on individual vs. group decision-making, in risky contexts, has brought about divergent results, mainly depending on the institutional rules through which groups take decisions. Some studies where group decisions relied on majority rule showed no appreciable difference between individuals and groups’ preferences, others where unanimity among group members was required found collective decisions to be less risk-averse than individual ones. We elicited groups’ preferences over risk using what we defined “endogenous-decision-rule”, i.e. leaving groups free to endogenously solve the potential disagreement among their members. Our results unambiguously show that individuals are more risk seeker than groups when facing gambles with positive expected payoff difference and more risk-averse in the opposite case.

Cooperative Stochastic Games with Mean-Variance Preferences

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.

Optimal Stopping in the Balls-and-Bins Problem

This paper considers a multistage balls-and-bins problem with optimal stopping connected with the job allocation model. There are N steps. The player drops balls (tasks) randomly one at a time into available bins (servers). The game begins with only one empty bin. At each step, a new bin can appear with probability p. At step n (n = 1, . . . ,N), the player can choose to stop and receive the payoff or continue the process and move to the next step. If the player stops, then he/she gets 1 for every bin with exactly one ball and loses 1/2 for every bin with two or more balls. Empty bins do not count. At the last step, the player must stop the process. The player's aim is to find the stopping rule which maximizes the expected payoff. The optimal payoff at each step are calculated. An approximate strategy depending on the number of steps is proposed. It is demonstrated that the payo when using this strategy is close to the optimal payoff.

An experiment on deception, reputation and trust

An experiment is designed to shed light on how deception works. The experiment involves a twenty period sender/receiver game in which period 5 has more weight than other periods. In each period, the informed sender communicates about the realized state, the receiver then reports a belief about the state before being informed whether the sender lied. Throughout the interaction, a receiver is matched with the same sender who is either malevolent with an objective opposed to the receiver or benevolent always telling the truth. The main findings are: (1) in several variants (differing in the weight of the key period and the share of benevolent senders), the deceptive tactic in which malevolent senders tell the truth up to the key period and then lie at the key period is used roughly 25% of the time, (2) the deceptive tactic brings higher expected payoff than other observed strategies, and (3) a majority of receivers do not show cautiousness at the key period when no lie was made before. These observations do not match the predictions of the Sequential Equilibrium and can be organized using the analogy-based sequential equilibrium (ABSE) in which three quarters of subjects reason coarsely.

The Valuator’s Curse: Decision Analysis of Overvaluation and Disappointment in Acquisition

Initial valuations of entrepreneurial ventures offering uncertain payoffs can often be overvalued by investors; namely, the expected payoff postacquisition is smaller than the expected payoff prior to acquisition when the investor harbors uncertainties about various components of the business. Common explanations involve irrationality such as psychological preference for potential over realized payoffs. We provide a different, rational explanation, which we term the valuator’s curse. It is similar in nature to the winner’s curse in auctions and the optimizer’s curse in decision analysis, but the source of the curse is neither from the competitive effects of an auction-type mechanism nor from the optimization effects in a choice among alternatives. Rather the effect is generated from the nonlinear evaluation of the payoffs, even though the inputs to the evaluation are unbiased. We formalize the valuator’s curse and discuss its implications to entrepreneur’s learning. The valuator’s curse proves a boon to the entrepreneur as it leads to larger capitalizations.