On a Simple Hedonic Game with Graph-Restricted Communication

International audienceWe study a hedonic game for which the feasible coalitions are prescribed by a graph representing the agents' social relations. A group of agents can form a feasible coalition if and only if their corresponding vertices can be spanned with a star. This requirement guarantees that agents are connected, close to each other, and one central agent can coordinate the actions of the group. In our game everyone strives to join the largest feasible coalition. We study the existence and computational complexity of both Nash stable and core stable partitions. Then, we provide tight or asymptotically tight bounds on their quality, with respect to both the price of anarchy and stability, under two natural social functions, namely, the number of agents who are not in a singleton coalition, and the number of coalitions. We also derive refined bounds for games in which the social graph is restricted to be claw-free. Finally, we investigate the complexity of computing socially optimal partitions as well as extreme Nash stable ones

Topological Price of Anarchy bounds for clustering games on networks

We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their choices with their neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs, which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds

On the macroeconomics of uncertainty and incomplete markets

Presidential address for the Twelfth World Congress of the International Economic Association, summarising semi-formally the author's recent work and concerns. Uncertainty and incomplete markets breed demand volatility as well as price and wage rigidities. The conjunction of these leads to multiple, volatile supply-constrained equilibria, typically reflecting coordination failures and apt to display persistence - as documented by three supporting theorems. Specific implications are linked to the conclusions that we should take coordination failures seriously, try to obviate demand volatility and try to by-pass price and wage rigidities

Arrow’s theorem of the deductible: moral hazard and stop-loss in health insurance

We show that the logic of Arrow's theorem of the deductible, i.e. that it is optimal to focus insurance coverage on the states with largest expenditures, remains at work in a model with ex post moral hazard. The optimal insurance contract takes the form of a system of "implicit deductibles", i.e. it results in the same indemnities as a contract with full insurance above a variable deductible positively related to the elasticity of medical expenditures with respect to the insurance rate. In a model with an explicit stop-loss arrangement, i.e. with a predefined ceiling on the annual expenses of the insured, this stop-loss takes the form of a deductible, i.e. there is no reimbursement for expenses below the stop-loss amount. One motivation to have some insurance below the deductible arises if regular health care expenditures in a situation of standard health have a negative effect on the probability of getting into a state with large medical expenses.status: publishe

Indeterminateness of equilibria and macroeconomics

The paper reviews results on indeterminateness of equilibria in two extensions of the standard (Arrow-Debreu) model of general equilibrium. These extensions, motivated by macroeconomic interpretations, concern money and price rigidities. In a natural extension to money (held for transaction purposes), if monetary policy fixes either nominal interest rates or money supply (but not both), the variability of inflation rates is unrestricted, at equilibrium. In the absence of initial nominal asset positions, the indeterminateness of inflation rates is harmless, in the complete-markets framework of Arrow-Debreu. When some relative prices are predetermined, there exists generically a continuum of real equilibria, indexed by the overall degree of rationing. In a model combining money and nominal price rigidities, the fixed nominal prices limit the indeterminateness of inflation rates, but the real indeterminateness subsits. When one introduces in addition a tatonnement process of nominal price formation, incorporatingsome downward nominal rigidities, both the nominal and the real indeterminateness may be eliminated (through the initial conditions), in the complete-markets framework. It is argued that macroeconomic interpretations call for an incomplete-markets framework, hence for expectations, another source of indeterminateness. A concludingsection offers some heuristic remarks on the open problems associated with market incompleteness