José Martins

Abstract
The notion of Union is strength is essential for preserving public goods and mitigating public bads such as air quality. International environmental agreements serve this role by forming stable coalitions, in which agents join or leave based on free-riding incentives. Building on the Baliga-Maskin model, we show that such coalitions can emerge from a simple Markov chain mechanism where agents enter or exit through utility-based bargaining. However, stable coalition formation is challenging, as members may receive substantially lower utility than free-riders. This asymmetry gives rise to Barrett's paradox of cooperation: even with large coalitions and strong preferences among free-riders, overall utility may remain far below that of the grand coalition. Encouragingly, the paradox of cooperation can be resolved when free-riders have sufficiently low preferences.

Abstract
We propose a statistical duality among the preferences and endowments of the agents. Under this duality, the logarithmic prices of random trades among agents in a decentralized economy converge in expectation to the logarithm of the Walrasian equilibrium price in a centralized economy.

Abstract
This paper fits in the theory of international agreements by studying the success of stable coalitions of agents seeking the preservation of a public good. Extending Baliga and Maskin, we consider a model of N homogeneous agents with quasi-linear utilities of the form u(j) (r(j); r) = r(alpha) - r(j), where r is the aggregate contribution and the exponent alpha is the elasticity of the gross utility. When the value of the elasticity alpha increases in its natural range (0, 1), we prove the following five main results in the formation of stable coalitions: (i) the gap of cooperation, characterized as the ratio of the welfare of the grand coalition to the welfare of the competitive singleton coalition grows to infinity, which we interpret as a measure of the urge or need to save the public good; (ii) the size of stable coalitions increases from 1 up to N; (iii) the ratio of the welfare of stable coalitions to the welfare of the competitive singleton coalition grows to infinity; (iv) the ratio of the welfare of stable coalitions to the welfare of the grand coalition decreases (a lot), up to when the number of members of the stable coalition is approximately N/e and after that it increases (a lot); and (v) the growth of stable coalitions occurs with a much greater loss of the coalition members when compared with free-riders. Result (v) has two major drawbacks: (a) A priori, it is difficult to convince agents to be members of the stable coalition and (b) together with results (i) and (iv), it explains and leads to the pessimistic Barrett's paradox of cooperation, even in a case not much considered in the literature: The ratio of the welfare of the stable coalitions against the welfare of the grand coalition is small, even in the extreme case where there are few (or a single) free-riders and the gap of cooperation is large. Optimistically, result (iii) shows that stable coalitions do much better than the competitive singleton coalition. Furthermore, result (ii) proves that the paradox of cooperation is resolved for larger values of.. so that the grand coalition is stabilized.

Abstract
Inspired by the Daley-Kendall and Goffman-Newill models, we propose an Ignorant-Believer-Unbeliever rumor (or fake news) spreading model with the following characteristics: (i) a network contact between individuals that determines the spread of rumors; (ii) the value (cost versus benefit) for individuals who search for truthful information (learning); (iii) an impact measure that assesses the risk of believing the rumor; (iv) an individual search strategy based on the probability that an individual searches for truthful information; (v) the population search strategy based on the proportion of individuals of the population who decide to search for truthful information; (vi) a payoff for the individuals that depends on the parameters of the model and the strategies of the individuals. Furthermore, we introduce evolutionary information search dynamics and study the dynamics of population search strategies. For each value of searching for information, we compute evolutionarily stable information (ESI) search strategies (occurring in non-cooperative environments), which are the attractors of the information search dynamics, and the optimal information (OI) search strategy (occurring in (eventually forced) cooperative environments) that maximizes the expected information payoff for the population. For rumors that are advantageous or harmful to the population (positive or negative impact), we show the existence of distinct scenarios that depend on the value of searching for truthful information. We fully discuss which evolutionarily stable information (ESI) search strategies and which optimal information (OI) search strategies eradicate (or not) the rumor and the corresponding expected payoffs. As a corollary of our results, a recommendation for legislators and policymakers who aim to eradicate harmful rumors is to make the search for truthful information free or rewarding.

Abstract
In this work, we introduce the concept of maximum curvature to separate the low from high reinfection levels. For each temporary immunity transition rate, the threshold value is the infection rate where the positive curvature of the endemic stationary state attains its maximum value. Hence, the maximum curvature reinfection threshold can be interpreted as the moment when the graph of the stationary state of infected attains the maximum change in its direction. When the temporary immunity transition rate tends to zero, the limiting point of the maximum curvature reinfection threshold coincides with the Gomes' reinfection threshold and the curvature blows up to infinity.