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1 . Territoriality Now, we wish to return to the Hawk - Dove model but to more closely tie this model to animal territoriality by
Territoriality
Now, we wish to return to the HawkDove model but to more closely tie this model to animal territoriality by introducing signals about which player arrived first. Well allow one player to arrive before the other, each player to get a signal of this, and allow players to condition their choice of action on their signal. We formalize as the following Bayesian Game:
A state of the world, omega is randomly chosen from the set Omega where represents the case where player arrived first, and the case where player arrived first. We will assume each state is equally likely. Players do not directly observe the state. Instead, each player, i receives a private signal si that is independently drawn from the set S Let si omega with probability epsi for some epsi in We can interpret epsi as the amount of noise in players signals, and epsi as the case where both players know, with certainty, who arrived first.
After a state, omega and signals, ss are drawn, players play the standard HawkDove game and can condition their action on their signal. Recall, the standard HawkDove game has the following payoffs matrix:
Hawk Hawk vcv
Dove v
Dove
v # v
Consider the Strategy profile where each player plays H if and only if they got the signal that they arrived first. I.esigma sigma where sigma isi i Hawk and sigma isi i Dove. We will call such a strategy the Territorial Strategy
a Start by assuming players know with certainty who arrived first, ieepsi Show that it is a Bayesian Nash Equilibrium, for both to play the Territorial Strategy.Territoriality
Now, we wish to return to the HawkDove model but to more closely tie this model to animal
territoriality by introducing 'signals' about which player arrived first. We'll allow one player
to arrive before the other, each player to get a signal of this, and allow players to condition
their choice of action on their signal. We formalize as the following Bayesian Game:
A state of the world, is randomly chosen from the set where represents the
case where player arrived first, and the case where player arrived first. We will assume
each state is equally likely. Players do not directly observe the state. Instead, each player,
receives a private signal that is independently drawn from the set Let
with probability for some We can interpret as the amount of noise in
players' signals, and as the case where both players know, with certainty, who arrived
first.
After a state, and signals, are drawn, players play the standard HawkDove game
and can condition their action on their signal. Recall, the standard HawkDove game has the
following payoffs matrix:
Consider the Strategy profile where each player plays if and only if they got the signal that
they arrived first. I.e where Hawk and Dove. We will call
such a strategy the 'Territorial Strategy'.
a Start by assuming players know with certainty who arrived first, ie Show that
it is a Bayesian Nash Equilibrium, for both to play the Territorial Strategy.
b Next consider an arbitrary value of Find conditions on and under which
it is a Bayesian Nash equilibrium for both to play the Territorial Strategy.
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