Optimal equilibria of the best shot game

We consider any network environment in which the "best shot game" is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game typically exhibits a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.Comment: submitted to JPE

On FO2 quantifier alternation over words

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels

Paying Positive to Go Negative: Advertisers' Competition and Media Reports

This paper analyzes a two-sided market for news where advertisers may pay a media outlet to conceal negative information about the quality of their own product (paying positive to avoid negative) and/or to disclose negative information about the quality of their competitors' products (paying positive to go negative). We show that whether advertisers have negative consequences on the accuracy of news reports or not ultimately depends on the extent of correlation among advertisers' products. Specifically, the lower the correlation among the qualities of the advertisers' products, the (weakly) higher the accuracy of the media outlet' reports. Moreover, when advertisers' products are correlated, a higher degree of competition in the market of the advertisers' products may decrease the accuracy of the media outlet's reports.

Collaboration in Social Networks

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria -- that we call "collaborative equilibria" -- that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks

Beta-blocker under-use in COPD patients

Background: Cardiovascular (CVS) comorbidities are common in COPD and contribute significantly to morbidity and mortality, especially following acute exacerbations of COPD (AECOPD). Beta-blockers (BBs) are safe and effective in COPD patients, with demonstrated survival benefit following myocardial infarction. We sought to determine if BBs are under-prescribed in patients hospitalized with AECOPD. We also sought to determine inpatient rates of CVS and cerebrovascular complications, and their impact on patient outcomes. Methods: Retrospective hospital data was collected over a 12-month period. The medical records of all patients 40 years of age coded with a diagnosis of AECOPD were analyzed. Prevalent use and incident initiation of BBs were assessed. Comorbidities including indications and contraindications for BB use were analyzed. Results: Of the 366 eligible patients, 156 patients (42.6%) had at least one indication for BB use – of these patients, only 53 (34.0%) were on BB therapy and 61 (39.1%) were not on BB therapy but had no listed contraindication. Prevalent use of BBs at the time of admission in all 366 patients was 19.7%, compared with 45.6%, 39.6% and 45.9% use of anti-platelets, statins and angiotensin-converting enzyme inhibitor/angiotensin II receptor blockers, respectively. CVS and cerebrovascular complications were common in this population (57 patients, 16%) and were associated with longer length of stay (p,0.01) and greater inpatient mortality (p=0.02). Conclusions: BBs are under-prescribed in COPD patients despite clear indication(s) for their use. Further work is required to explore barriers to BB prescribing in COPD patients

Pattern formation and optimization in army ant raids

Army ant colonies display complex foraging raid patterns involving thousands of individuals communicating through chemical trails. In this paper we explore, by means of a simple search algorithm, the properties of these trails in order to test the hypothesis that their structure reflects an optimized mechanism for exploring and exploiting food resources. The raid patterns of three army ant species, {em Eciton hamatum}, {em Eciton burchelli} and {em Eciton rapax}, are analysed. The respective diets of these species involve large but rare, small but common, and a combination of large but rare and small but common, food sources. Using a model proposed by Deneubourg and collaborators, we simulate the formation of raid patterns in response to different food distributions. Our results indicate that the empirically observed raid patterns maximise return on investment, that is, the amount of food brought back to the nest per unit of energy expended, for each of the diets. Moreover, the values of the parameters that characterise the three optimal pattern-generating mechanisms are strikingly similar. Therefore the same behavioural rules at the individual level can produce optimal colony-level patterns. The evolutionary implications of these findings are discussed.Postprint (published version