My research focuses on evolutionary dynamics in structured populations, with broader applications to mathematical biology and complex systems.
Frontiers
Evolutionary dynamics of collective decision-making.
Every collective decision shapes the future population composition.
The population might be swarms choosing nests, employees setting strategies, or electorates voting for policies.
A group's choice alters the environment, which causes selection pressures to change, which leads to a different population.
Under repeated decisions, which collective procedures sustain an adaptable population?
The cost of trust.
Trust relies on information about others, and no individual gets that information without cost.
At one extreme, the pessimist who demands cryptographic proof asks for almost no trust but requires high computational costs.
At the other extreme, the blind optimist asks for almost nothing costly and trusts mostly everything, a form of faith.
Between them, the price is paid in memory, computation, communication, and time spent waiting.
How cheap can a trust protocol get before cooperation collapses?
The ethology of nobodies.
Soon most human interaction will be mediated by artificial agents acting on our behalf.
The norms we rely on to cooperate were built for beings who feel shame, hold grudges, cannot be identically replicated, et cetera.
In contrast, artificial agents are dissociative.
They are assembled from modular parts, their traits are configurable, and strangely, their identity does not persist.
Reputation is ungrounded and punishment is undeliverable.
Agents that cannot be held to account are morally unmoored and systemically dangerous.
Which norms are substrate-independent, and which have to be revised, rebuilt, or invented?
Info
I received an SM in applied mathematics from Harvard.
I completed my BS degrees in mathematics and computer science at UIUC
where I conducted research in biophysics, algebraic combinatorics, and theoretical computer science.
Before graduate school I spent time as a software engineer and a quant at various tech and trading firms.
My work is supported by a Harvard Graduate Prize Fellowship.
Direct reciprocity in the donation game, played with discount factor δ (the probability of another round).
A cooperator bestows a recepient a benefit b but pays a cost c; a defector neither gifts nor pays any costs.
Selection favors Tit-for-Tat (TFT) above the curve δ∗ = c/((b−c)x + c)
and Always Defect (ALLD) below it, so the interior equilibrium x∗ = c(1−δ)/(δ(b−c))
is unstable.
Thus direct reciprocity can lead to the evolution of cooperation only when δ > c/b.
Drawn for b/c = 3.
The boxed equation is the quasispecies system of n coupled equations, one per type,
for n types with frequencies xi, fitnesses fi and
mutation matrix Q = [qij], where
ϕ = ∑ixifi is average
fitness; Q = I gives no mutation, and fi depending on
x is frequency-dependent selection. It is the simplest complete description of
evolutionary dynamics. Taken from my
replicator
equation + direct reciprocity lecture for MATH 243.
