Research map / Multi-agent systems and games / Games and equilibria
Trade-Offs Between Information and Crowding in Sequential Decisions (Student Abstract)
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Studies sequential decisions where agents choose among options with public signals and shared payoffs that shrink with crowding, using a polynomial-time dynamic programming algorithm to compute equilibrium strategies and proving non-monotonicity and convergence results.
Problem
Sequential decision-making (herding-style models) where agents balance informational effects of predecessors' choices against crowding effects from splitting a fixed payoff among those who pick the same option.
Approach
Extends information-cascade models with crowding: a winning option's value is divided among all correct guessers, so earlier choices carry information but also reduce later payoffs. A polynomial-time dynamic programming algorithm computes equilibrium strategies for large games with public signals, revealing non-monotone behavior.
Key results
- For n=3 and p < 2-√2, the first player who draws a blue marble optimally guesses MR rather than MB, contrary to naive symmetry reasoning.
- Theorem 1: the probability of guessing MB is non-increasing in the number of previous MB guesses.
- Theorem 2: after J(n)=β log_{q/p}(n) players (β>1), the probability that player j guesses correctly tends to 1 as n grows.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Account for payoff crowding when choosing between urn states | Sequential urn-guessing game · Urn model | probability of guessing correctly | Mixed |
| Increase the number of previous MB guesses | Optimal sequential strategy · Urn model | probability of guessing MB | Hurt |
| Use the optimal strategy after O(log n) guesses | Sequential urn-guessing game · Urn model | probability of guessing correctly | Helped |
| Wait until O(log n) guesses have been made | Sequential urn-guessing game · Urn model | expected number of incorrect guesses | Helped |
Surprising findings
- The first player may guess the less likely urn color (MR) after drawing a blue marble because crowding costs outweigh the benefit of the more likely option.
- Agents sometimes choose options with lower expected crowding over options with better informational or current crowding properties.
Limitations
- Characterization of early agents' alternating decisions is left open.
- Analysis is for a simplified two-option urn model with public signals.
Experimental setup
Metrics: optimal guess probability probability of correct guess
Builds on: information cascade models (Banerjee 1992; Bikhchandani, Hirshleifer, Welch 1992 Acemoglu et al. 2008
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