Titel Timing Games

page) which can hold a single value, a stream of readers (customers)
that arrive at a constant rate in the time interval $[0,1]$, and a
set of writers (advertisers) that each write to the shared register
one time. If we interpret the value of the shared register as an
advertisement, or a pointer a reader can follow to an interesting
resource, then each writer's goal is to maximize the time its value
is in the register. We analyze this scenario as a strategic timing
game. Each player (corresponding to a writer) $i$ chooses a point
$x_i\in[0,1]$. The utility to player $i$ is the distance from its
point $x_i$ to the next larger point, or to $1$ if $x_i$ is the
largest, and each player's goal is to maximize the length of this
interval. We fully characterize the Nash equilibrium for the
two-player, continuous-action game, and we give an efficient
algorithm to compute the symmetric Nash equilibrium for the
$n$-player, discrete-action game. In both cases, we show that the
(symmetric) equilibrium is unique. Our algorithmic approach to the
$n$-player game is an interesting one, since equilibria to
two-player games can usually be found by solving differential
equations, but equilibria to $n$-player games often involve systems
of partial differential equations that are much harder to solve.