Game Theory, Misc

Certain apparently simple problems of coming to an agreement are surprisingly difficult to analyze in terms of individually rational behavior with a given set of preferences and beliefs. Though initially the solution appears obvious, the reasoning that would be needed to reach the solution on the part of a pair of rational individuals seems baroque and doubtful. This is used to suggest that a more fruitful tack is to analyze the situation in terms of a kind of joint or shared (...) intentionality. If that can be invoked, what appears simple in practice will turn out to be simple in theory as well. (shrink)

In this article I interpret resilience and evolution in view of the philosophy of Leibniz. First, I discuss resilience as a substance’s or a monad’s “quantity of essence” — its “degree of perfection” — which I express as the quality of the Whole with respect to the sum of the qualities of the Parts. Then I discuss evolution, which I interpret here as the autopoietic Principle that sets Itself in motion and creates all reality, including Itself. This Principle may be (...) considered as a sort of ante-litteram metaphysical Darwinian Selection. My interpretations provide a different formulation for questions such as “why natural evolution evolves?” and “why is this the best of all possible worlds?” In this article I also provide a geometrical interpretation of a key aspect behind the “divine mathematics” of the autopoietic Principle. (shrink)

A critique of John Rawls' gamification of justice.

This paper develops an argument against causal decision theory. I formulate a principle of preference, which I call the Guaranteed Principle. I argue that the preferences of rational agents satisfy the Guaranteed Principle, that the preferences of agents who embody causal decision theory do not, and hence that causal decision theory is false.

A survey of some game-theoretic accounts of the emergence and evolution of spontaneuous cooperation in social and public-good dilemmas.

Recent work on the resource curse argues that the effect of resource wealth on development outcomes is a conditional one: resource dependent countries with low quality institutions are vulnerable to a resource curse, while resource dependent countries with high quality institutions are not. But extant models neglect the ways in which the inflow of resource revenue impacts the institutional environment itself. In this paper, I present a formal model to show that where domestic institutions do not limit state leaders' discretion (...) over policy prior to becoming fiscally reliant on resources, those leaders have little incentive in the wake of resource windfalls to establish institutional mechanisms that limit their discretion. Importantly, this shows that simple calls for domestic institutional reform are unlikely to be effective. Among other things, future prescriptions to mitigate the resource curse must focus on decreasing rulers' fiscal reliance on resources. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the principles (...) that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

Decision theory is concerned with how agents should act when the consequences of their actions are uncertain. The central principle of contemporary decision theory is that the rational choice is the choice that maximizes subjective expected utility. This entry explains what this means, and discusses the philosophical motivations and consequences of the theory. The entry will consider some of the main problems and paradoxes that decision theory faces, and some of responses that can be given. Finally the entry will briefly (...) consider how decision theory applies to choices involving more than one agent. (shrink)

We evaluate the asymptotic performance of boundedly-rational strategies in multi-armed bandit problems, where performance is measured in terms of the tendency (in the limit) to play optimal actions in either (i) isolation or (ii) networks of other learners. We show that, for many strategies commonly employed in economics, psychology, and machine learning, performance in isolation and performance in networks are essentially unrelated. Our results suggest that the appropriateness of various, common boundedly-rational strategies depends crucially upon the social context (if any) (...) in which such strategies are to be employed. (shrink)

Pascal’s Wager holds that one has pragmatic reason to believe in God, since that course of action has infinite expected utility. The mixed strategy objection holds that one could just as well follow a course of action that has infinite expected utility but is unlikely to end with one believing in God. Monton (2011. Mixed strategies can’t evade Pascal’s Wager. Analysis 71: 642–45.) has argued that mixed strategies can’t evade Pascal’s Wager, while Robertson (2012. Some mixed strategies can evade Pascal’s (...) Wager: a reply to Monton. Analysis 72: 295–98.) has argued that Monton is mistaken. We show that Monton is correct, highlight the crucial assumptions that he relies on, and shed some light on the role of mixed strategies in decision theory. (shrink)

The paper focuses on Anthony de Jasay's "anarcho-liberalism" as based oon his game-theoretic approach to the problem of public goods provision.

This is the introductory essay to the Italian translation of Anthony de Jasay's "Choice, contract, and consent. A restatement of liberalism".

In this article we explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this is empirically (...) true: i.e. that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance with this pattern in the 18th century and how it recurred in the 1950s when Allais made his case against the neo-Bernoullians. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The (...) measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)

We trace the difference between the ways in which apes and humans co–operate to differences in communicative abilities, claiming that the pressure for future–directed co–operation was a major force behind the evolution of language. Competitive co–operation concerns goals that are present in the environment and have stable values. It relies on either signalling or joint attention. Future–directed co–operation concerns new goals that lack fixed values. It requires symbolic communication and context–independent representations of means and goals. We analyse these ways of (...) co–operating in game–theoretic terms and submit that the co–operative strategy of games that involve shared representations of future goals may provide new equilibrium solutions. (shrink)

An introduction to the special issue on epistemic logic and the foundations of game theory edited by Michael Bacharach and Philippe Mongin. Contributors are Michael Bacharach, Robert Stalnaker, Salvatore Modica and Aldo Rustichini, Luc Lismont and Philippe Mongin, and Hyun-Song Shin and Timothy Williamson.

The Prisoner's Dilemma (PD) exhibits a tragedy in this sense: if the players are fully informed and rational, they are condemned to a jointly dispreferred outcome. In this essay I address the following question: What feature of the PD's payoff structure is necessary and sufficient to produce the tragedy? In answering it I use the notion of a trembling-hand equilibrium. In the final section I discuss an implication of my argument, an implication which bears on the persistence of the problem (...) posed by the PD. (shrink)

I argue in this paper that there are two considerations which govern the dynamics of a two-person bargaining game, viz. relative proportionate utility loss from conceding to one's opponent's proposal and relative non-proportionate utility loss from not conceding to one's opponent's proposal, if she were not to concede as well. The first consideration can adequately be captured by the information contained in vNM utilities. The second requires measures of utility which allow for an interpersonal comparison of utility differences. These considerations (...) respectively provide for a justification of the Nash solution and the Kalai egalitarian solution. However, none of these solutions taken by themselves can provide for a full story of bargaining, since, if within a context of bargaining one such consideration is overriding, the solution which does not match this consideration will yield unreasonable results. I systematically present arguments to the effect that each justification from self-interest for respectively the Nash and the Kalai egalitarian solution is vulnerable to this kind of objection. I suggest that the search for an integrative model may be a promising line of research. (shrink)