Research map / Learning theory and algorithms / Submodular and game algorithms
Competition among Pairwise Lottery Contests
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Studies competition among multiple pairwise lottery contests where designers pick two of n contestants and set biases, proving contestant equilibrium existence/uniqueness via an equilibrium multiplier vector and designer equilibrium existence under substage or divisible-prize settings.
Problem
Two-stage competition in which contest designers choose participant pairs, prizes and biases for pairwise lottery contests, while contestants allocate effort across contests; existence and computation of subgame perfect equilibria.
Approach
Introduces an equilibrium multiplier vector (Lagrange-style marginal utility per contestant) to characterize all contestant equilibria, proves its existence via Brouwer and uniqueness via a monotone property, and shows designer equilibria exist under two-substage or divisible-prize settings.
Key results
- Proves existence and uniqueness of the equilibrium multiplier vector for any designer strategy profile, fully characterizing contestant equilibria.
- Shows a polynomial-time algorithm computes an epsilon-approximate contestant equilibrium.
- Shows a weak designer equilibrium always exists in the indivisible prize model, while a designer equilibrium may fail to exist there; in the divisible prize model a designer equilibrium exists when max_i T_i <= half the total effort.
Surprising findings
- In the indivisible prize model the designer equilibrium may not exist, because changing participants can change optimal biases.
- Setting balancing biases (1/2 winning probability) is not a dominant strategy for designers in the second substage.
Limitations
- Analysis restricted to two participants per contest and the lottery CSF rather than general Tullock CSF.
- Designer equilibrium not guaranteed in the indivisible prize model under simultaneous decisions.
Experimental setup
Builds on: Colonel Blotto games Tullock contest weighted congestion game Brouwer fixed-point theorem
Closest papers by meaning
- Understanding Over Participation in Simple Contests (AAAI 2018 · similarity 0.87)
- From Monopoly to Competition: Optimal Contests Prevail (AAAI 2023 · similarity 0.86)
- From Duels to Battlefields: Computing Equilibria of Blotto and Other Games (AAAI 2016 · similarity 0.86)
- Dueling over Dessert, Mastering the Art of Repeated Cake Cutting (NeurIPS 2024 · similarity 0.86)
- Smooth Partial Lotteries for Stable Randomized Selection (NeurIPS 2026 · similarity 0.84)
- Cost Minimization for Equilibrium Transition (AAAI 2024 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.