Budget-Constrained Multi-Battle Contests: A New Perspective and Analysis

In a multi-battle contest, each time a player competes by investing some of her budgets or resources in a component battle to collect a value if winning the battle. There are multiple battles to fight, and the budgets get consumed over time. The final winner in the overall contest is the one who first reaches some amount of total value. Examples include R & D races, sports competition, elections, and many more. A player needs to make adequate sequential actions to win the contest against dynamic competition over time from the others. We are interested in how much budgets the players would need and what actions they should take in order to perform well.
We model and study such budget-constrained multi-battle contests where each component battle is a first-price or all-pay auction. We focus on analyzing the 2-player budget ratio that guarantees a player's winning (or falling behind in just a bounded amount of collected value) against the other omnipotent player. In the settings considered, we give efficient dynamic programs to find the optimal budget ratios and the corresponding bidding strategies. Our definition of game, budget constraints, and emphasis on budget analyses provide a new perspective and analysis in the related context.