  Proof-of-Work is a consensus algorithm where miners solve cryptographic
puzzles to mine blocks and obtain a reward through some Block Reward Mechanism
(BRM). PoW blockchain faces the problem of centralization due to the formation
of mining pools, where miners mine blocks as a group and distribute rewards.
The rationale is to reduce the risk (variance) in reward while obtaining the
same expected block reward. In this work, we address the problem of
centralization due to mining pools in PoW blockchain. We propose a two-player
game between the new miner joining the system and the PoW blockchain system.
  We model the utility for the incoming miner as a combination of (i) expected
block reward, (ii) risk, and (iii) cost of switching between different mining
pools. With this utility structure, we analyze the equilibrium strategy of the
incoming miner for different BRMs: (a) memoryless -- block reward is history
independent (e.g., Bitcoin) (b) retentive: block reward is history-dependent
(e.g., Fruitchains). For memoryless BRMs, we show that depending on the
coefficient of switching cost $c$, the protocol is decentralized when $c = 0$
and centralized when $c > \underline{c}$. In addition, we show the
impossibility of constructing a memoryless BRM where solo mining gives a higher
payoff than forming/joining mining pools. While retentive BRM in Fruitchains
reduces risk in solo mining, the equilibrium strategy for incoming miners is
still to join mining pools, leading to centralization. We then propose our
novel retentive BRM -- \textsf{Decent-BRM}. We show that under
\textsf{Decent-BRM}, incoming miners obtain higher utility in solo mining than
joining mining pools. Therefore, no mining pools are formed, and the Pow
blockchain using \textsf{Decent-BRM} is decentralized.
