Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Convergence Rates of Blockchain Mining Games: A Markovian Approach   Understanding the strategic behavior of miners in a blockchain is of great
importance for its proper operation. A common model for mining games considers
an infinite time horizon, with players optimizing asymptotic average
objectives. Implicitly, this assumes that the asymptotic behaviors are realized
at human-scale times, otherwise invalidating current models. We study the
mining game utilizing Markov Decision Processes. Our approach allows us to
describe the asymptotic behavior of the game in terms of the stationary
distribution of the induced Markov chain. We focus on a model with two players
under immediate release, assuming two different objectives: the (asymptotic)
average reward per turn and the (asymptotic) percentage of obtained blocks.
  Using tools from Markov chain analysis, we show the existence of a strategy
achieving slow mixing times, exponential in the policy parameters. This result
emphasizes the imperative need to understand convergence rates in mining games,
validating the standard models. Towards this end, we provide upper bounds for
the mixing time of certain meaningful classes of strategies. This result yields
criteria for establishing that long-term averaged functions are coherent as
payoff functions. Moreover, by studying hitting times, we provide a criterion
to validate the common simplification of considering finite states models. For
both considered objectives functions, we provide explicit formulae depending on
the stationary distribution of the underlying Markov chain. In particular, this
shows that both mentioned objectives are not equivalent. Finally, we perform a
market share case study in a particular regime of the game. More precisely, we
show that an strategic player with a sufficiently large processing power can
impose negative revenue on honest players.

3
The categories of this paper are: physics
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int