Discrete-Time Strategic Experimentation

In many real-world economic scenarios, agents must allocate resources between highrisk,high-reward options and safer, more predictable alternatives. Their decisions evolveas new information becomes available, creating a tension between exploration (seekingnew opportunities) and exploitation (capitalizing on known outcomes). This explorationexploitationtrade-off is captured by the bandit problem, where agents choose betweendifferent "arms," each representing an uncertain option. This exploration-exploitationtrade-off is particularly significant in industries where innovation and researchintensity drive success, such as pharmaceuticals, and AI technology.Despite extensive research, existing theoretical bandit models often rely on continuoustimeframeworks and discrete choice sets or convex/linear payoff functions, leading tobinary predictions where agents either fully commit to experimentation or haltexploration altogether. In reality, decision variables (time and budget) are perfectlydivisible, and resource allocation is periodically adjusted, revealing a gap between thesemodels and practical decision-making. This disconnect raises concerns about theapplicability of traditional models and the validity of their implications.This project aims to address these limitations by investigating a multi-agentexploration-exploitation trade-off in strategic environments with discrete time andcontinuous decision variables. We introduce a novel approach to overcome the reciprocityissue inherent in the bandit problem by defining both actions and beliefs as statevariables, and using a process function to characterize their evolution process. Thisflexible framework captures the dynamics of strategic interactions more effectively thantraditional methods.Agents in these settings must also consider how their actions will influence and beinfluenced by others. For example, firms may make decisions while accounting for thestrategies of competitors. Our preliminary results suggest continuous, non-binaryallocations, with exploration continuing until constrained by external factors such asdeadlines. This approach significantly improves resource allocation strategies, leading toa higher likelihood of breakthroughs and increased expected payoffs. These insights canoptimize innovation cycles and enhance budget planning for industries reliant on highrisk,high-reward projects.Key practical questions explored in this project include: How much should each agentinvest when others are also experimenting? Will breakthroughs be shared publicly orkept private, and how will this affect competition? Will some agents emerge as leaders ininnovation while others "free ride" on their efforts? Can policymakers enhance outcomesby offering dynamic contracts that adjust incentives over time? This project providesdeeper insights into strategic experimentation, offering a more practical understandingthan existing models and yielding implications to optimize resource allocation and fosterefficient innovation.