Socially Optimal Mining Pools

Mining for Bitcoins is a high-risk high-reward activity. Miners, seeking to reduce their variance and earn steadier rewards, collaborate in pooling strategies where they jointly mine for Bitcoins. Whenever some pool participant is successful, the earned rewards are appropriately split among all pool participants. Currently a dozen of different pooling strategies (i.e., methods for distributing the rewards) are in use for Bitcoin mining. We here propose a formal model of utility and social welfare for Bitcoin mining (and analogous mining systems) based on the theory of discounted expected utility, and next study pooling strategies that maximize the social welfare of miners. Our main result shows that one of the pooling strategies actually employed in practice--the so-called geometric pay pool--achieves the optimal steady-state utility for miners when its parameters are set appropriately. Our results apply not only to Bitcoin mining pools, but any other form of pooled mining or crowdsourcing computations where the participants engage in repeated random trials towards a common goal, and where "partial" solutions can be efficiently verified

Does timing of decisions in a mixed duopoly matter?

We determine the endogenous order of moves in a mixed pricesetting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payo equivalence of the games with an exogenously given order of moves if the most plausible equilibrium is realized in the market. Hence, in this case it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand-Edgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists

The UN in the lab

We consider two alternatives to inaction for governments combating terrorism, which we term Defense and Prevention. Defense consists of investing in resources that reduce the impact of an attack, and generates a negative externality to other governments, making their countries a more attractive objective for terrorists. In contrast, Prevention, which consists of investing in resources that reduce the ability of the terrorist organization to mount an attack, creates a positive externality by reducing the overall threat of terrorism for all. This interaction is captured using a simple 3×3 “Nested Prisoner’s Dilemma” game, with a single Nash equilibrium where both countries choose Defense. Due to the structure of this interaction, countries can benefit from coordination of policy choices, and international institutions (such as the UN) can be utilized to facilitate coordination by implementing agreements to share the burden of Prevention. We introduce an institution that implements a burden-sharing policy for Prevention, and investigate experimentally whether subjects coordinate on a cooperative strategy more frequently under different levels of cost sharing. In all treatments, burden sharing leaves the Prisoner’s Dilemma structure and Nash equilibrium of the game unchanged. We compare three levels of burden sharing to a baseline in a between-subjects design, and find that burden sharing generates a non-linear effect on the choice of the efficient Prevention strategy and overall performance. Only an institution supporting a high level of mandatory burden sharing generates a significant improvement in the use of the Prevention strategy

Game theory of mind

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution

Free choice activates a decision circuit between frontal and parietal cortex

We often face alternatives that we are free to choose between. Planning movements to select an alternative involves several areas in frontal and parietal cortex that are anatomically connected into long-range circuits. These areas must coordinate their activity to select a common movement goal, but how neural circuits make decisions remains poorly understood. Here we simultaneously record from the dorsal premotor area (PMd) in frontal cortex and the parietal reach region (PRR) in parietal cortex to investigate neural circuit mechanisms for decision making. We find that correlations in spike and local field potential (LFP) activity between these areas are greater when monkeys are freely making choices than when they are following instructions. We propose that a decision circuit featuring a sub-population of cells in frontal and parietal cortex may exchange information to coordinate activity between these areas. Cells participating in this decision circuit may influence movement choices by providing a common bias to the selection of movement goals

Stimmensplitting und Koalitionswahl

Hat sich die Unabhängigkeitsstrategie der FDP bei der letzten Bundestagswahl ausgezahlt? Wäre die FDP erfolgreicher gewesen, wenn sie im Vorfeld klar signalisiert hätte, dass man eine Koalition mit der Union anstrebt? Wie war das bei den Grünen, die ja im Gegensatz zur FDP keine Zweifel aufkommen ließen? Natürlich können wir nicht wie in einer Simulation oder einem Experiment einfach den Wahlkampf wiederholen und noch einmal wählen lassen. Um eine befriedigende Antwort auf diese Frage zu finden, vergleichen wir den Kontext der Bundestagswahl 2002 mit den zurückliegenden Bundestagswahlen. Aus dem Längsschnittvergleich versuchen wir Rückschlüsse auf den substanziellen Einfluss von strategischem Stimmensplitting im Sinne einer Koalitionswahl auf das Wahlergebnis gerade der kleinen Parteien zu ziehen. Um unsere Forschungsfrage zu beantworten und substanzielle Schlüsse ziehen zu können, muss zuerst klar sein, in welcher Form und warum Stimmensplitting relevant sein kann, welche Rolle dabei Koalitionsabsprachen vor einer jeden Wahl spielen und, schließlich, welche alternativen Erklärungsmöglichkeiten die Literatur zum Thema Stimmensplitting und strategischem Wählen anzubieten hat. Nur wenn wir auch die Wirkung alternativer und zum Teil konkurrierender Hypothesen zulassen, können wir unserer Schlußfolgerungen sicher sein

Priority for the Worse Off and the Social Cost of Carbon

The social cost of carbon (SCC) is a monetary measure of the harms from carbon emission. Specifically, it is the reduction in current consumption that produces a loss in social welfare equivalent to that caused by the emission of a ton of CO2. The standard approach is to calculate the SCC using a discounted-utilitarian social welfare function (SWF)—one that simply adds up the well-being numbers (utilities) of individuals, as discounted by a weighting factor that decreases with time. The discounted-utilitarian SWF has been criticized both for ignoring the distribution of well-being, and for including an arbitrary preference for earlier generations. Here, we use a prioritarian SWF, with no time-discount factor, to calculate the SCC in the integrated assessment model RICE. Prioritarianism is a well-developed concept in ethics and theoretical welfare economics, but has been, thus far, little used in climate scholarship. The core idea is to give greater weight to well-being changes affecting worse off individuals. We find substantial differences between the discounted-utilitarian and non-discounted prioritarian SCC

Moral hazard in marriage: the use of domestic labor as an incentive device

This paper argues that some women in developing countries use domestic labor as a tool to incentivize husbands. A theoretical model is derived based on the traditions of rural Malawi, where men often supplement farm income with wage labor. As wage labor is not observed by the wife, this creates moral hazard: husbands may not make enough effort to bring home wages. The model predicts that women overcome this by using domestic labor as an incentive device: they increase their domestic labor and reduce their leisure in response to good consumption outcomes, but only if they cannot rely on divorce threat as an alternative source of incentives. This prediction is confirmed using survey data from Malawi. Identification is based on the fact that Malawi's kinship traditions exogenously determine women's accessibility to divorce. Where divorce is not an option, women make inefficient labor choices in order to provide incentives

Are groups more rational than individuals? A review of interactive decision making in groups

Many decisions are interactive; the outcome of one party depends not only on its decisions or on acts of nature but also on the decisions of others. In the present article, we review the literature on decision making made by groups of the past 25 years. Researchers have compared the strategic behavior of groups and individuals in many games: prisoner's dilemma, dictator, ultimatum, trust, centipede and principal-agent games, among others. Our review suggests that results are quite consistent in revealing that groups behave closer to the game-theoretical assumption of rationality and selfishness than individuals. We conclude by discussing future research avenues in this area