A Multi-Faceted Approach to Understand How Resource Diversity Can Mediate the Coexistence of Cryptic Marine Nematode Species

Based on the principle of competitive exclusion, species occupying the same ecological niche cannot stably coexist due to strong interspecific competition for resources. Niche diversification, for instance through resource partitioning, may alleviate competition. Here, we investigate the effects of resource diversity on foraging behavior, fitness and interspecific interactions of four cryptic bacterivorous nematode species (Pm I–IV) of the Litoditis marina species complex with sympatric field distributions. Three resource (bacteria) diversity levels (low, medium, high) were used as food treatments and compared to a treatment with only Escherichia coli as food. Differences in taxis to food existed between the cryptic species and between bacterial mixtures of different diversity: all the cryptic species except Pm I showed higher attraction toward medium-diversity food. Furthermore, the cryptic species of L. marina generally exhibited higher fitness on a more diverse food resource. Resource diversity also impacted the interspecific interactions between the cryptic species. Our results show that resource diversity can alter the interspecific interactions among the cryptic species of L. marina, indicating that competitive equilibria between species are very context-dependent. Although a considerable body of evidence supports the hypotheses (e.g., “variance-in-edibility” hypothesis and the “dilution hypothesis” or “resource concentration hypothesis”) which predict a negative impact on consumers when resource diversity is increased, the benefits of a diverse resource can outweigh these disadvantages by offering a more complete and/or complementary range of nutritional resources as suggested by the “balanced diet” hypothesis.

Fairness and fuzzy coalitions

In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

Sustainable debt

We show that debt is sustainable at a competitive equilibrium based solely on the reputation for repayment; that is, even without collateral or legal sanctions available to creditors. In an incomplete asset market, when the rate of interest falls recurrently below the rate of growth of the economy, self‐insurance is more costly than borrowing, and repayments on loans are enforced by the implicit threat of loss of the risk‐sharing advantages of debt contracts. Private debt credibly circulates as a form of inside money, and it is not valued as a speculative bubble. Competitive equilibria with self‐enforcing debt exist under a suitable hypothesis of gains from trade.

Competitive Equilibrium and Trading Networks: A Network Flow Approach

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.

Equilibrium, Efficiency, and Welfare

Competitive equilibria are studied in both partial-equilibrium and general-equilibrium settings for economies characterized by consumers with incomplete preference structures. Market equilibrium determination is developed as solving a zero-maximum problem for a supremal convolution whose dual, by Fenchel's Duality Theorem, coincides with a zero-minimum for an infimal convolution that characterizes Pareto optima. The First and Second Welfare Theorems are natural consequences. The maximization of the sum of consumer surplus and producer surplus is studied in this analytic setting, and the implications of nonsmooth preference structures or technologies for equilibrium determination are discussed.