Equilibria of the Colonel Blotto Games with Costs

Authors: Stanisław Kaźmierowski

AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section, we report on the carried-out experiments, focusing on the amount of resources players obtain in equilibrium. First, we provide a high-level description of the implemented program, used for finding the lower (upper) bound on the number of resources obtained in equilibrium. Second, we report and discuss the obtained results. Lastly, we report the running times of our program.
Researcher Affiliation Academia Stanisław Ka zmierowski University of Warsaw EMAIL
Pseudocode Yes Algorithm 1 describes the idea of our implementation. Formally, Algorithm 1 returns a linear program describing an optimal strategy of the Colonel Blotto game with sunk costs B(DA, DB, n + 1, ˆv). ... Algorithm 2 describes the high-level idea of computing the maximal (minimal) expected number of resources in any equilibrium strategy of player A of the Colonel Blotto game with costs.
Open Source Code No Our implementation was done in C++, using the state-of-the-art Gurobi (Gurobi Optimization, LLC 2022) LP-optimizer.
Open Datasets No The paper defines the game and its parameters (DA, DB, n, v, c A, c B, g A, g B) and describes setting up models with linear or squared costs. It does not mention using any external, publicly available datasets.
Dataset Splits No The paper does not mention using or splitting any datasets. The experiments involve simulating a game with varying parameters rather than processing an existing dataset with defined splits.
Hardware Specification Yes We ran the code on a machine with an Apple M3 Pro processor unit and an 18-GB memory.
Software Dependencies No Our implementation was done in C++, using the state-of-the-art Gurobi (Gurobi Optimization, LLC 2022) LP-optimizer.
Experiment Setup Yes In the first setting, we considered linear obtainment costs with unit costs of a resource equal to 0.05 and no assignment costs. Hence, the payoff ˆπ to player P is ... In the second setting, we considered squared assignment costs with a coefficient of 0.01 and no obtainment costs. Hence, the payoff π to player P is ...