Where do mistakes lead? A survey of games with incompetent players

Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings

Mistakes can stabilise the dynamics of rock-paper-scissors games

A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium

Prioritised learning in snowdrift-type games

Cooperation is a ubiquitous and beneficial behavioural trait despite being prone to exploitation by free-riders. Hence, cooperative populations are prone to invasions by selfish individuals. However, a population consisting of only free-riders typically does not survive. Thus, cooperators and free-riders often coexist in some proportion. An evolutionary version of a Snowdrift Game proved its efficiency in analysing this phenomenon. However, what if the system has already reached its stable state but was perturbed due to a change in environmental conditions? Then, individuals may have to re-learn their effective strategies. To address this, we consider behavioural mistakes in strategic choice execution, which we refer to as incompetence. Parametrising the propensity to make such mistakes allows for a mathematical description of learning. We compare strategies based on their relative strategic advantage relying on both fitness and learning factors. When strategies are learned at distinct rates, allowing learning according to a prescribed order is optimal. Interestingly, the strategy with the lowest strategic advantage should be learnt first if we are to optimise fitness over the learning path. Then, the differences between strategies are balanced out in order to minimise the effect of behavioural uncertainty

The Theory of Money and Financial Institutions

A sketch of a game theoretic approach to the Theory of Money and Financial Institutions is presented in a nontechnical, nonmathematical manner. The detailed argument and specifics are presented in previous articles and in a forthcoming book.

Necessary Conditions for Improving Civic Competence: A Scientific Perspective

Many attempts to increase civic competence are based on premises about communication and belief change that are directly contradicted by important insights from microeconomic theory and social psychology. At least two economic literatures are relevant to my effort to improve matters. One is the literature on strategic communication, which includes Spence (1974), Crawford and Sobel (1982), Banks (1991), and Lupia and McCubbins (1998). The other is the literature on mechanism design, which includes Green and Laffont (1977), Myerson (1983) and Palfrey (1992). While both literatures have the potential to convey important insights, many scholars and practitioners do not yet see a need for such insights. This paper lays such a foundation. It explains how greater attention to basic scientific principles can help people who want to increase civic competence use the generosity of donors and the hard work of well-intentioned citizens more effectively. The paper continues as follows. First, I discuss the topic of competence more precisely. Then, I introduce the necessary conditions for increasing civic competence described above. Next, I describe implications and applications of these conditions – focusing in this paper on the growing contention that deliberation is an effective way to increase civic competence. Applying the necessary conditions to this topic reveals a need to revise and clarify common expectations about what deliberation can accomplish. A brief concluding section follows.incomplete information, strategic communication, learning, behavioral economics,

Does consultation improve decision making?

This paper reports an experiment designed to test whether prior consultation within a group affects subsequent individual decision making in tasks where demonstrability of correct solutions is low. In our experiment subjects considered two paintings created by two different artists and were asked to guess which artist made each painting. We observed answers given by individuals under two treatments: in one, subjects were allowed the opportunity to consult with other participants before making their private decisions; in the other there was no such opportunity. Our primary findings are that subjects in the first treatment evaluate the opportunity to consult positively but they perform significantly worse and earn significantly less.Consultation; Decision making; Group decisions; Individual decisions

The Communicative Character of Capitalistic Competition: A Hayekian response to the Habermasian challenge

"Ideal speech situations", "domination-free discourse" or "deliberative communities" describe political ideals proudly cherished by many sociologists. The sometimes explicit, sometimes implicit, motivation is to mobilise political discourse as an instrument to tame or transform the capitalistic "system" according to alleged needs of "society". Most economists and defenders of capitalistic competition, in return, don?t care about communicative communities. The individual market actor is assumed or demanded to be free to choose among given alternatives satisfying given preferences subject to given constraints. Why, then, should homo oeconomicus argue (van Aaken 2003)? There is no "communicative action" among the individuals that populate economic textbooks, there is only "commutative action". Only a few, mostly "Austrian", economists realised that the exchange of goods and services within the spontaneous order of "catallaxy" involves an exchange of knowledge, ideas, opinions, expectations, and arguments – that markets are indeed communicative networks (e.g. Hayek 1946/48; Lavoie, ed. 1991; Horwitz 1992). In fact, and this will be my major claim, market competition is more "deliberative" than politics in the sense that more information about available social problem solutions and their comparative performance, about people's preferences, ideas and expectations is spontaneously created, disseminated and tested. This very idea is anathema for followers of Habermasian discourse ethics. The intellectual thrust and political clout of their vindication of deliberative politics critically seems to depend on a mostly tacit assumption that markets fail to address social needs and regulate social conflicts. Political discourse therefore ?steps in to fill the functional gaps when other mechanisms of social integration are overburdened? (Habermas 1996: 318). I will claim that the argument should be very much the other way around: politics and public deliberations are overburdened mechanisms – unable to deal with an increasingly complex and dynamic society. Moreover, the requisites of ideal speech communities are so enormous that functional gaps are inevitable. Partly, these gaps can be closed if market competition steps in. Partly, reorganisations of the political system are needed. Hence, I am not arguing that Habermas is wrong by stressing the need for open discourse in order to reach informed agreement among citizens who seek to realise mutual gains from joint commitment by contributing to common (public) goods and submitting to common rules of conduct (s.a. Vanberg 2003). I am challenging his neglect of capitalistic competition as a communicative device and his disdain for the classical liberal conception of bounded democracy that respects individual property rights (e.g. Habermas 1975; 1998). --