33 research outputs found
Oceanic Games: Centralization Risks and Incentives in Blockchain Mining
To participate in the distributed consensus of permissionless blockchains,
prospective nodes -- or miners -- provide proof of designated, costly
resources. However, in contrast to the intended decentralization, current data
on blockchain mining unveils increased concentration of these resources in a
few major entities, typically mining pools. To study strategic considerations
in this setting, we employ the concept of Oceanic Games, Milnor and Shapley
(1978). Oceanic Games have been used to analyze decision making in corporate
settings with small numbers of dominant players (shareholders) and large
numbers of individually insignificant players, the ocean. Unlike standard
equilibrium models, they focus on measuring the value (or power) per entity and
per unit of resource} in a given distribution of resources. These values are
viewed as strategic components in coalition formations, mergers and resource
acquisitions. Considering such issues relevant to blockchain governance and
long-term sustainability, we adapt oceanic games to blockchain mining and
illustrate the defined concepts via examples. The application of existing
results reveals incentives for individual miners to merge in order to increase
the value of their resources. This offers an alternative perspective to the
observed centralization and concentration of mining power. Beyond numerical
simulations, we use the model to identify issues relevant to the design of
future cryptocurrencies and formulate prospective research questions.Comment: [Best Paper Award] at the International Conference on Mathematical
Research for Blockchain Economy (MARBLE 2019
Monopoly Pricing in a Vertical Market with Demand Uncertainty
We study a vertical market with an upsteam supplier and multiple downstream
retailers. Demand uncertainty falls to the supplier who acts first and sets a
uniform wholesale price before the retailers observe the realized demand and
engage in retail competition. Our focus is on the supplier's optimal pricing
decision. We express the price elasticity of expected demand in terms of the
mean residual demand (MRD) function of the demand distribution. This allows for
a closed form characterization of the points of unitary elasticity that
maximize the supplier's profits and the derivation of a mild unimodality
condition for the supplier's objective function that generalizes the widely
used increasing generalized failure rate (IGFR) condition. A direct implication
is that optimal prices between different markets can be ordered if the markets
can be stochastically ordered according to their MRD functions or equivalently
to their elasticities. Based on this, we apply the theory of stochastic orders
to study the response of the supplier's optimal price to various features of
the demand distribution. Our findings challenge previously established economic
insights about the effects of market size, demand transformations and demand
variability on wholesale prices and indicate that the conclusions largely
depend on the exact notion that will be employed. We then turn to measure
market performance and derive a distribution free and tight bound on the
probability of no trade between the supplier and the retailers. If trade takes
place, our findings indicate that ovarall performance depends on the interplay
between demand uncertainty and level of retail competition
On the Mean Residual Life of Cantor-Type Distributions: Properties and Economic Applications
In this paper, we consider the mean residual life (MRL) function of the
Cantor distribution and study its properties. We show that the MRL function is
continuous at all points, locally decreasing at all points outside the Cantor
set and has a unique fixed point which we explicitly determine. These
properties readily extend to the parametric family of p-singular, Cantor type
distributions introduced by Mandelbrot (1983). The findings offer evidence
that, contrary to common perceptions, Cantor-type distributions are tractable
enough to be considered for practical applications. We provide such an example
from the field of economics in which Cantor-type distributions can be used to
model markets with recurrent bandwagon effects and show that earlier
anticipated bandwagon effects lead to higher monopolistic prices. We conclude
with a simple implementation of the algorithm by Chalice (1991) to plot
Cantor-type distributions
Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory
Exploration-exploitation is a powerful and practical tool in multi-agent
learning (MAL), however, its effects are far from understood. To make progress
in this direction, we study a smooth analogue of Q-learning. We start by
showing that our learning model has strong theoretical justification as an
optimal model for studying exploration-exploitation. Specifically, we prove
that smooth Q-learning has bounded regret in arbitrary games for a cost model
that explicitly captures the balance between game and exploration costs and
that it always converges to the set of quantal-response equilibria (QRE), the
standard solution concept for games under bounded rationality, in weighted
potential games with heterogeneous learning agents. In our main task, we then
turn to measure the effect of exploration in collective system performance. We
characterize the geometry of the QRE surface in low-dimensional MAL systems and
link our findings with catastrophe (bifurcation) theory. In particular, as the
exploration hyperparameter evolves over-time, the system undergoes phase
transitions where the number and stability of equilibria can change radically
given an infinitesimal change to the exploration parameter. Based on this, we
provide a formal theoretical treatment of how tuning the exploration parameter
can provably lead to equilibrium selection with both positive as well as
negative (and potentially unbounded) effects to system performance.Comment: Appears in the 35th AAAI Conference on Artificial Intelligenc