32 research outputs found
On the expected number of equilibria in a multi-player multi-strategy evolutionary game
In this paper, we analyze the mean number of internal equilibria in
a general -player -strategy evolutionary game where the agents' payoffs
are normally distributed. First, we give a computationally implementable
formula for the general case. Next we characterize the asymptotic behavior of
, estimating its lower and upper bounds as increases. Two important
consequences are obtained from this analysis. On the one hand, we show that in
both cases the probability of seeing the maximal possible number of equilibria
tends to zero when or respectively goes to infinity. On the other hand,
we demonstrate that the expected number of stable equilibria is bounded within
a certain interval. Finally, for larger and , numerical results are
provided and discussed.Comment: 26 pages, 1 figure, 1 table. revised versio
Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games
In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, fn,dfn,d, and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as √d−1 as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained
On Equilibrium Properties of the Replicator–Mutator Equation in Deterministic and Random Games
In this paper, we study the number of equilibria of the replicator-mutator
dynamics for both deterministic and random multi-player two-strategy
evolutionary games. For deterministic games, using Decartes' rule of signs, we
provide a formula to compute the number of equilibria in multi-player games via
the number of change of signs in the coefficients of a polynomial. For
two-player social dilemmas (namely, the Prisoner's Dilemma, Snowdrift, Stag
Hunt, and Harmony), we characterize (stable) equilibrium points and
analytically calculate the probability of having a certain number of equilibria
when the payoff entries are uniformly distributed. For multi-player random
games whose payoffs are independently distributed according to a normal
distribution, by employing techniques from random polynomial theory, we compute
the expected or average number of internal equilibria. In addition, we perform
extensive simulations by sampling and averaging over a large number of possible
payoff matrices to compare with and illustrate analytical results. Numerical
simulations also suggest several interesting behaviour of the average number of
equilibria when the number of players is sufficiently large or when the
mutation is sufficiently small. In general, we observe that introducing
mutation results in a larger average number of internal equilibria than when
mutation is absent, implying that mutation leads to larger behavioural
diversity in dynamical systems. Interestingly, this number is largest when
mutation is rare rather than when it is frequent.Comment: 23 page
On the distribution of the number of internal equilibria in random evolutionary games
In this paper, we study the distribution of the number of internal equilibria
of a multi-player two-strategy random evolutionary game. Using techniques from
the random polynomial theory, we obtain a closed formula for the probability
that the game has a certain number of internal equilibria. In addition, by
employing Descartes' rule of signs and combinatorial methods, we provide useful
estimates for this probability. Finally, we also compare our analytical results
with those obtained from samplings.Comment: 31 pages, comments are welcome. arXiv admin note: substantial text
overlap with arXiv:1708.0167
Eliciting patients’ health concerns in consulting rooms and wards in Vietnamese public hospitals
This article examines the doctor’s elicitation of the patient’s presenting health concern in two clinical settings in the Vietnamese public hospital system: the consulting room and the ward. The data were taken from 66 audio-recorded consultations. Our analysis shows that the elicitors used by the doctor in the consulting room often communicate a weak epistemic stance towards the patient’s health issue, while those used in the ward tend to signal a strong epistemic stance. In addition, this contrast between the elicitors employed in the consulting room and the ward is evident in our data regardless of whether the consultation is a first visit or a same follow-up (in which the doctor is the same one that treated the patient on their last visit), though the contrast is less clear for different follow-ups (in which the doctor has not treated the patient before). An additional finding is that the clinical setting has some bearing on the use of inappropriate elicitation formats (in which the doctor opens the visit with an elicitor which is more appropriate for another type of visit). The precise way in which each of the consulting room and the ward operates is, of course, a feature of the Vietnamese public hospital system itself. Hence, the overall contrast between the elicitors and elicitation formats used in these two settings illustrates how, on a more general level, the institutional context can have an impact on doctor-patient communication
Cost efficiency of institutional incentives for promoting cooperation in finite populations
Institutions can provide incentives to increase cooperation behaviour in a
population where this behaviour is infrequent. This process is costly, and it
is thus important to optimize the overall spending. This problem can be
mathematically formulated as a multi-objective optimization problem where one
wishes to minimize the cost of providing incentives while ensuring a desired
level of cooperation within the population. In this paper, we provide a
rigorous analysis for this problem. We study cooperation dilemmas in both the
pairwise (the Donation game) and multi-player (the Public Goods game) settings.
We prove the regularity of the (total incentive) cost function, characterize
its asymptotic limits (infinite population, weak selection and large selection)
and show exactly when reward or punishment is more efficient. We prove that the
cost function exhibits a phase transition phenomena when the intensity of
selection varies. We calculate the critical threshold in regards to the phase
transition and study the optimization problem when the intensity of selection
is under and above the critical value. It allows us to provide an exact
calculation for the optimal cost of incentive, for a given intensity of
selection. Finally, we provide numerical simulations to demonstrate the
analytical results. Overall, our analysis provides for the first time a
selection-dependent calculation of the optimal cost of institutional incentives
(for both reward and punishment) that guarantees a minimum amount of
cooperation. It is of crucial importance for real-world applications of
institutional incentives since intensity of selection is specific to a given
population and the underlying game payoff structure.Comment: preliminary versio