Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-frequency limit of Nash equilibria in a market impact game with
  transient price impact   We study the high-frequency limits of strategies and costs in a Nash
equilibrium for two agents that are competing to minimize liquidation costs in
a discrete-time market impact model with exponentially decaying price impact
and quadratic transaction costs of size $\theta\ge0$. We show that, for
$\theta=0$, equilibrium strategies and costs will oscillate indefinitely
between two accumulation points. For $\theta>0$, however, strategies, costs,
and total transaction costs will converge towards limits that are independent
of $\theta$. We then show that the limiting strategies form a Nash equilibrium
for a continuous-time version of the model with $\theta$ equal to a certain
critical value $\theta^*>0$, and that the corresponding expected costs coincide
with the high-frequency limits of the discrete-time equilibrium costs. For
$\theta\neq\theta^*$, however, continuous-time Nash equilibria will typically
not exist. Our results permit us to give mathematically rigorous proofs of
numerical observations made in Schied and Zhang (2013). In particular, we
provide a range of model parameters for which the limiting expected costs of
both agents are decreasing functions of $\theta$. That is, for sufficiently
high trading speed, raising additional transaction costs can reduce the
expected costs of all agents.

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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: adap-org