Escaping the Tragedy of the Commons through Targeted Punishment

Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread cooperation is often much more difficult. We show here that there exist strategies of `targeted punishment' whereby a small number of punishers can shift a population of defectors into a state of global cooperation. The heterogeneity of players, often regarded as an obstacle, can in fact boost the mechanism's effectivity. We conclude by outlining how the international community could use a strategy of this kind to combat climate change.Comment: Manuscript plus Supplementary Materia

Calabi-Yau threefolds with large h^{2, 1}

We carry out a systematic analysis of Calabi-Yau threefolds that are elliptically fibered with section ("EFS") and have a large Hodge number h^{2, 1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of moduli space associated with different topologies connected through transitions that can be understood in terms of singular Weierstrass models. We determine the complete set of such threefolds that have h^{2, 1} >= 350 by tuning coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set of Hodge numbers includes those of all known Calabi-Yau threefolds with h^{2, 1} >= 350, as well as three apparently new Calabi-Yau threefolds. We speculate that there are no other Calabi-Yau threefolds (elliptically fibered or not) with Hodge numbers that exceed this bound. We summarize the theoretical and practical obstacles to a complete enumeration of all possible EFS Calabi-Yau threefolds and fourfolds, including those with small Hodge numbers, using this approach.Comment: 44 pages, 5 tables, 5 figures; v2: minor corrections; v3: minor corrections, moved figure; v4: typo in Table 2 correcte

Inequality and Network Formation Games

This paper addresses the matter of inequality in network formation games. We employ a quantity that we are calling the Nash Inequality Ratio (NIR), defined as the maximal ratio between the highest and lowest costs incurred to individual agents in a Nash equilibrium strategy, to characterize the extent to which inequality is possible in equilibrium. We give tight upper bounds on the NIR for the network formation games of Fabrikant et al. (PODC '03) and Ehsani et al. (SPAA '11). With respect to the relationship between equality and social efficiency, we show that, contrary to common expectations, efficiency does not necessarily come at the expense of increased inequality.Comment: 27 pages. 4 figures. Accepted to Internet Mathematics (2014

Algorithm Instance Games

This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of the algorithm's description influence agents' strategic behavior? We analyze two versions of an AIG based on the set-cover optimization problem. In these games, joint strategies correspond to instances of the set-cover problem, with each subset (of a given universe of elements) representing the strategy of a single agent. Outcomes are covers computed from the joint strategies by a set-cover algorithm. In one variant of this game, outcomes are computed by a deterministic greedy algorithm, and the other variant utilizes a non-deterministic form of the greedy algorithm. We characterize Nash equilibrium strategies for both versions of the game, finding that agents' strategies can vary considerably between the two settings. In particular, we find that the version of the game based on the deterministic algorithm only admits Nash equilibrium in which agents choose strategies (i.e., subsets) containing at most one element, with no two agents picking the same element. On the other hand, in the version of the game based on the non-deterministic algorithm, Nash equilibrium strategies can include agents with zero, one, or every element, and the same element can appear in the strategies of multiple agents.Comment: 14 page

Robust short-term memory without synaptic learning

Short-term memory in the brain cannot in general be explained the way long-term memory can -- as a gradual modification of synaptic weights -- since it takes place too quickly. Theories based on some form of cellular bistability, however, do not seem able to account for the fact that noisy neurons can collectively store information in a robust manner. We show how a sufficiently clustered network of simple model neurons can be instantly induced into metastable states capable of retaining information for a short time (a few seconds). The mechanism is robust to different network topologies and kinds of neural model. This could constitute a viable means available to the brain for sensory and/or short-term memory with no need of synaptic learning. Relevant phenomena described by neurobiology and psychology, such as local synchronization of synaptic inputs and power-law statistics of forgetting avalanches, emerge naturally from this mechanism, and we suggest possible experiments to test its viability in more biological settings.Comment: 20 pages, 9 figures. Amended to include section on spiking neurons, with general rewrit

Spectral Properties of H-Reflex Recordings After an Acute Bout of Whole-Body Vibration

Although research supports the use of whole-body vibration (WBV) to improve neuromuscular performance, the mechanisms for these improvements remain unclear. The purpose of this study was to identify the effect ofWBV on the spectral properties of electrically evoked H-reflex recordings in the soleus (SOL) muscle. The H-reflex recordings were measured in the SOL muscle of 20 participants before and after a bout of WBV. The H-reflexes were evoked every 15 seconds for 150 seconds after WBV. A wavelet procedure was used to extract spectral data, which were then quantified with a principle components analysis. Resultant principle component scores were used for statistical analysis. The analysis extracted 1 principle component associated with the intensity of the myoelectric spectra and 1 principle component associated with the frequency. The scores of the principle component that were related to the myoelectric intensity were smaller at 30 and 60 milliseconds after WBV than before WBV. The WBV transiently decreased the intensity of myoelectric spectra during electrically evoked contractions, but it did not influence the frequency of the spectra. The decrease in intensity likely indicates a smaller electrically evoked muscle twitch response, whereas the lack of change in frequency would indicate a similar recruitment pattern of motor units before and after WBV