In a multi-battle contest, each time a player competes by investing some ofher budgets or resources in a component battle to collect a value if winningthe battle. There are multiple battles to fight, and the budgets get consumedover time. The final winner in the overall contest is the one who first reachessome amount of total value. Examples include R & D races, sports competition,elections, and many more. A player needs to make adequate sequential actions towin the contest against dynamic competition over time from the others. We areinterested in how much budgets the players would need and what actions theyshould take in order to perform well. We model and study such budget-constrained multi-battle contests where eachcomponent battle is a first-price or all-pay auction. We focus on analyzing the2-player budget ratio that guarantees a player's winning (or falling behind injust a bounded amount of collected value) against the other omnipotent player.In the settings considered, we give efficient dynamic programs to find theoptimal budget ratios and the corresponding bidding strategies. Our definitionof game, budget constraints, and emphasis on budget analyses provide a newperspective and analysis in the related context.
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