arXiv subjects

Hangxin Gan

Publications and source records attributed to Hangxin Gan.

3 recordsLinked to original sources

arXiv2024

Equilibrium Analysis of Customer Attraction Games

We introduce a game model called "customer attraction game" to demonstrate the competition among online content providers. In this model, customers exhibit interest in various topics. Each content provider selects one topic and benefits from the attracted customers. We investigate both symmetric and asymmetric settings involving agents and customers. In the symmetric setting, the existence of pure Nash equilibrium (PNE) is guaranteed, but finding a PNE is PLS-complete. To address this, we propose a fully polynomial time approximation scheme to identify an approximate PNE. Moreover, the tight Price of Anarchy (PoA) is established. In the asymmetric setting, we show the nonexistence of PNE in certain instances and establish that determining its existence is NP-hard. Nevertheless, we prove the existence of an approximate PNE. Additionally, when agents select topics sequentially, we demonstrate that finding a subgame-perfect equilibrium is PSPACE-hard. Furthermore, we present the sequential PoA for the two-agent setting.

cs.GT↗

arXiv2023

Competition among Pairwise Lottery Contests

We investigate a two-stage competitive model involving multiple contests. In this model, each contest designer chooses two participants from a pool of candidate contestants and determines the biases. Contestants strategically distribute their efforts across various contests within their budget. We first show the existence of a pure strategy Nash equilibrium (PNE) for the contestants, and propose a polynomial-time algorithm to compute an $ε$-approximate PNE. In the scenario where designers simultaneously decide the participants and biases, the subgame perfect equilibrium (SPE) may not exist. Nonetheless, when designers' decisions are made in two substages, the existence of SPE is established. In the scenario where designers can hold multiple contests, we show that the SPE exists under mild conditions and can be computed efficiently.

cs.GT↗

arXiv2023

Approximate Nash Equilibria Algorithms for Shapley Network Design Games

We consider a weighted Shapley network design game, where selfish players choose paths in a network to minimize their cost. The cost function of each edge in the network is affine linear with respect to the sum of weights of the players who choose the edge. We first show the existence of α-approximate pure Nash equilibrium by constructing a potential function and establish an upper bound O(log2(W)) of α, where W is the sum of the weight of all players. Furthermore, we assume that the coefficients of the cost function (affine linear function) of the edge all are ϕ-smooth random variables on [0, 1]. In this case, we show that ε-best response dynamics can compute the (1 + ε)α-approximate pure Nash equilibrium (εis a positive constant close to 0) in polynomial time by proving the expected number of iterations is polynomial in 1/ε, ϕ, the number of players and the number of edges in the network.

cs.GT↗