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We study the competition and the evolution of nodes embedded in Euclidean restricted spaces. The population evolves by a branching process in which new nodes are generated when up to two new nodes are attached to the previous ones at each…
We study a class of semi-discrete variational problems that arise in economic matching and game theory, where agents with continuous attributes are matched to a finite set of outcomes with a one dimensional structure. Such problems appear…
We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the…
We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify…
We study the revenue-maximizing mechanism when a buyer's value evolves endogenously because of learning-by-consuming. A seller sells one unit of a divisible good, while the buyer relies on his private, rough valuation to choose his…
Most online platforms strive to learn from interactions with users, and many engage in exploration: making potentially suboptimal choices for the sake of acquiring new information. We study the interplay between exploration and competition:…
Involution now refers to the phenomenon that competitors in the same field make more efforts to struggle for limited resources but get lower individual ''profit effort ratio''. In this work, we investigate the evolution of the involution…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the…
In this paper, we consider the diffusive competition problem consisting of an invasive species with density $u$ and a native species with density $v$. We assume that $v$ undergoes diffusion and growth in $[0, \infty)$, and $u$ exists…
This paper investigates the impacts of competition in autonomous mobility-on-demand systems. By adopting a network-flow based formulation, we first determine the optimal strategies of profit-maximizing platform operators in monopoly and…
As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and…
By analyzing the duopoly market of computer graphics cards, we categorized the effects of enterprise's technological progress into two types, namely, cost reduction and product diversification. Our model proved that technological progress…
Evolution is based on the assumption that competing players update their strategies to increase their individual payoffs. However, while the applied updating method can be different, most of previous works proposed uniform models where…
Dynamic pricing of goods in a competitive environment to maximize revenue is a natural objective and has been a subject of research over the years. In this paper, we focus on a class of markets exhibiting the substitutes property with…
We study a stochastic differential game in a ruin theoretic environment. In our setting two insurers compete for market share, which is represented by a joint performance functional. Consequently, one of the insurers strives to maximize it,…
This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…
Privacy is an essential issue in data trading markets. This work uses a mechanism design approach to study the optimal market model to economize the value of privacy of personal data, using differential privacy. The buyer uses a finite…
I characterize the consumer-optimal market segmentation in competitive markets where multiple firms selling differentiated products to consumers with unit demand. This segmentation is public---in that each firm observes the same market…
In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends…