3,251 research outputs found
Supermodularity and preferences
We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation
Exploiting Weak Supermodularity for Coalition-Proof Mechanisms
Under the incentive-compatible Vickrey-Clarke-Groves mechanism, coalitions of
participants can influence the auction outcome to obtain higher collective
profit. These manipulations were proven to be eliminated if and only if the
market objective is supermodular. Nevertheless, several auctions do not satisfy
the stringent conditions for supermodularity. These auctions include
electricity markets, which are the main motivation of our study. To
characterize nonsupermodular functions, we introduce the supermodularity ratio
and the weak supermodularity. We show that these concepts provide us with tight
bounds on the profitability of collusion and shill bidding. We then derive an
analytical lower bound on the supermodularity ratio. Our results are verified
with case studies based on the IEEE test systems
Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor
The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply, supermodularity
A copula-based approach to aggregation functions
This paper presents the role of copula functions in the theory of aggregation operators and an axiomatic characterization of Archimedean aggregation functions. In this context we are focusing our attention about several properties of aggregation functions, like supermodularity and Schur-concavity.Aggregation functions, supermodularity, Schur-concavity, copula, Archimedean copulae
Innovation Complementarity and Scale of Production
complementarity; supermodularity; non-observed heterogeneity; product innovation; process innovation
Profit maximization and supermodular technology
A dataset is a list of observed factor inputs and prices for a technology; profits and production levels are unobserved. We obtain necessary and sufficient conditions for a dataset to be consistent with profit maximization under a monotone and concave revenue based on the notion of cyclic monotonicity. Our result implies that monotonicity and concavity cannot be tested, and that one cannot decide if a firm is competitive based on factor demands. We also introduce a condition, cyclic supermodularity, which is both necessary and sufficient for data to be consistent with a supermodular technology. Cyclic supermodularity provides a test for complementarity of production factors
When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting
This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. Previous work has identified theoretical conditions under which various stylized learning processes achieve convergence. One technical condition is supermodularity, which is closely related to the more familiar concept of strategic complementarities. We experimentally investigate the role of supermodularity in achieving convergence through learning. Using a game from the literature on solutions to externalities, we systematically vary a free parameter below, close to, at and beyond the threshold of supermodularity to assess its effects on convergence. We find that supermodular and ¡°near-supermodular¡± games converge significantly better than those far below the threshold. From a little below the threshold to the threshold, the improvement is statistically insignificant. Within the class of supermodular games, increasing the parameter far beyond the threshold does not significantly improve convergence. Simulation shows that while most experimental results persist in the long run, some become more pronounced.learning, supermodular games
Iterated weak dominance and interval-dominance supermodular games
This paper extends Milgrom and Robert's treatment of supermodular games in two ways. It points out that their main characterization result holds under a weaker assumption. It refines the arguments to provide bounds on the set of strategies that survive iterated deletion of weakly dominated strategies. I derive the bounds by iterating the best-response correspondence. I give conditions under which they are independent of the order of deletion of dominated strategies. The results have implications for equilibrium selection and dynamic stability in games
Designing Coalition-Proof Reverse Auctions over Continuous Goods
This paper investigates reverse auctions that involve continuous values of
different types of goods, general nonconvex constraints, and second stage
costs. We seek to design the payment rules and conditions under which
coalitions of participants cannot influence the auction outcome in order to
obtain higher collective utility. Under the incentive-compatible
Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are
achieved if the submitted bids are convex and the constraint sets are of a
polymatroid-type. These conditions, however, do not capture the complexity of
the general class of reverse auctions under consideration. By relaxing the
property of incentive-compatibility, we investigate further payment rules that
are coalition-proof without any extra conditions on the submitted bids and the
constraint sets. Since calculating the payments directly for these mechanisms
is computationally difficult for auctions involving many participants, we
present two computationally efficient methods. Our results are verified with
several case studies based on electricity market data
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