Many economic and social situations can be represented by a digraph. Both axiomatic and iterativemethods to determine the strength or power of all the nodes in a digraph have been proposed inthe literature. We propose a new method, where the power of a node is determined by both thenumber of its...

This paper develops necessary and sufficient conditions for monotone comparative statics predictions in several classes of stochastic optimization problems. The results are formulated so as to highlight the tradeoffs between assumptions about payoff functions and assumptions about probability...

We introduce a class of games with complementarities that has the quasisupermodular games, hence the supermodular games, as a special case. Our games retain the main property of quasisupermodular games: the Nash set is a nonempty complete lattice. We use monotonicity properties on the best reply...

The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities....

In the context of a continuum of random variables, arising, for example, as rates of return in financial markets with a continuum of assets, or as individual responses in games with a continuum of players, an important economic issue is to show how idiosyncratic risk can be removed through some...

Understanding whether preferences are sensitive to the frame has been a major topic of debate in the last decades. For example, several works have explored whether the dictator game in the give frame gives rise to a different rate of pro-sociality than the same game in the take frame, leading to...

We introduce the algorithmic learning equations (ALEs), a set of ordinary differential equations which characterizes the finite-time and asymptotic behaviour of the stochastic interaction between state-dependent learning algorithms in dynamic games. Our framework allows for a variety of...

We consider the n-player houseswapping game of Shapley-Scarf (1974), with indfferences in preferences allowed. It is well-known that the strict core of such a game may be empty, single-valued, or multi-valued. We define a condition on such games called "segmentability", which means that the set...

We study marriage problems where two groups of agents match to each other and probabilistic assignments are possible. When only ordinal preferences are observable, an extensively studied efficiency notion is stochastic dominance efficiency (sd-efficiency). First, we provide a characterization of...

Repeated interactions provide a prominent but paradoxical hypothesis for human cooperation in one-shot interactions. Intergroup competitions provide a different hypothesis that is intuitively appealing but heterodox. We show that neither mechanism reliably supports the evolution of cooperation...