Successful signaling can evolve in a signaling game faster and more reliably if the agents are equipped with a more sophisticated learning dynamics than simple reinforcement. But if one can show how it is possible for a particular feature of language to evolve by means of a very low-rationality form of learning like simple reinforcement, then the explanation is more generic and hence more compelling. Assuming agents who learn by simple reinforcement does not require one to ap- peal to special features of the agents that are well-tuned to the particular task at hand. Further, insofar as more sophisticated learning dynamics are typically able to recapitulate the successes of such low-rationality dynamics, showing that a particular feature of language use can evolve on simple reinforcement learning shows that it can evolve on a broad class of stronger learning dynamics. Finally, among low-rationality learning dynamics, simple reinforcement has the virtue that the evolution of the agents’ dispositions correspond to the evolution of strategy types in a population on the replicator dynamics, which allows one to translate the **evolutionary** results from one’s learning models to corresponding population models. 5

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The extended contests considered in our model are of a particular kind, namely contests where each individual has a set of potential exit points, and at each point it decides whether to continue, making a suitable investment, or concede the resource to its opponent. This is thus reminiscent of the classical war of attrition [2,3], but with discrete stages which are sequential, and so our game does not have this aspect of symmetry of the war of attrition. This leads to a completely different character of solution, where the war of attrition has a **probability** density function over the stopping times, our individuals either concede with **probability** 1 or do not concede (although in the contests with an uncertain finish time, the time of the contest follows a **probability** distribution due to a natural random contest duration). We note that when other asymmetries, e.g. of reward values or costs, or even of perceived role [18,31] are considered, mixed strategies similarly disappear (they are only maintained through, for example, uncertainty of role).

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On the star, whenever there are at least N = 5 vertices, an increase of the population size increases the average fixation **probability** of a randomly placed mutant Hawk. This is in contrast to the situation on the circle or complete graph, where the increase in the population size always yields lower fixation **probability**, see Figures 3a) and 3b). This difference is due to the fact that on the star, a Dove has a higher fitness than a neighbouring Hawk in very few cases, moreover only in those where the fixation of the Hawk is already very likely (if N is not small). Indeed, if a Dove is in the center, then its fitness is no more than d = 15/2 while the fitness of a Hawk on a leaf is b = 10. If a Dove is on a leaf with a Hawk in the center, then the fitness of the Dove is c = 5 while the fitness of the Hawk ranges from b = 10 (with no other Hawks in the population, i.e. when there is the highest danger of Hawk extinction), continuously going down to almost a (if there are Hawks on almost all other leaves, i.e. when Hawks are almost fixed in the population). Note that in our example this argument does not hold for small N, and the expected pattern of declining fixation **probability** with population size happens on the star as well, initially.

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We study the influence of complex graphs on the metastability and fixation properties of a set of **evolutionary** processes. In the framework of **evolutionary** game theory, where the fitness and selection are frequency dependent and vary with the population composition, we analyze the dynamics of snowdrift **games** (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system’s metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the **probability** and mean time of fixation are characterized by stretched-exponential behaviors with exponents depending on the network’s degree distribution.

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It is clear that in continuous models the **probability** of two independent events occurring within a given time interval tends to zero as the length of the time interval tends to zero. However, we should remember that biological reality can be very complicated and the outcomes of a single event can be very complex. For example, consider a male involved in a mating conflict where victory will lead to an immediate mating opportunity, i.e. there is a chain of conditional stages caused by a single interaction event. He may be killed instantly during a fight, or survive then mate successfully and die afterwards due to infection of his wounds. Death has occurred in both cases, but in the second case mating has also occurred, and it is important to distinguish the two different types of mortality. A similar idea has been known in population genetics for a long time (Prout 1965).

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We study the combined influence of selection and random fluctuations on the **evolutionary** dynam- ics of two-strategy (“cooperation” and “defection”) **games** in populations comprising cooperation facilitators. The latter are individuals that support cooperation by enhancing the reproductive po- tential of cooperators relative to the fitness of defectors. By computing the fixation **probability** of a single cooperator in finite and well-mixed populations that include a fixed number of facilitators, and by using mean field analysis, we determine when selection promotes cooperation in the impor- tant classes of prisoner’s dilemma, snowdrift and stag-hunt **games**. In particular, we identify the circumstances under which selection favors the replacement and invasion of defection by cooper- ation. Our findings, corroborated by stochastic simulations, show that the spread of cooperation can be promoted through various scenarios when the density of facilitators exceeds a critical value whose dependence on the population size and selection strength is analyzed. We also determine under which conditions cooperation is more likely to replace defection than vice versa.

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Even when **games** are pairwise, linearity only occurs because opponents are cho- sen at random, with equal **probability**. If some opponents are more likely than oth- ers and this is in any way related to the strategy of those involved, either through individuals directly being more likely to interact with those choosing a particular strategy or because evolution has led to different strategy distributions in differ- ent geographical locations, then nonlinearity will result, as we saw in Taylor and Nowak (2006). An example of this phenomenon occurs in food-stealing **games**, see e.g. Broom et al (2004, 2008).

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This model of judgement aggregation uses Boolean logic, which is only appropriate if each juror holds her **truth**-valuation with absolute certainty. However, these **truth**- valuations contradict one other, so at least one juror must be wrong —hence at least one juror cannot really be ‘certain’ in her beliefs. Indeed, outside of mathematics, there is really no sphere of knowledge where people can make assertions with absolute certainty. Normally each person has some degree of ‘confidence’ in a belief —a subjective **probability** which is strictly between zero and one —based on the quantity and quality of evidence available to her.

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As discussed in the Introduction, evidence **games** may have many equilibria; we are interested in those in which **truth** enjoys a certain prominence. This is expressed in two ways. First, if it is optimal for the agent to reveal the whole **truth**, then he prefers to do so (this holds for instance when the agent has a “lexicographic” preference: he always prefers a higher reward, but if the reward is the same whether he tells the whole **truth** or not, he prefers to tell the whole **truth**). Second, there is an infinitesimal **probability** that the whole **truth** is revealed (which happens, for example, when the agent is not strategic and instead always reveals his information; or, when there are “trembles,” such as a slip of the tongue, or of the pen, or a document that is attached by mistake, or the surfacing of an unexpected piece of evidence). To formalize this we use a standard limit-of-small-perturbations approach. Specifically, given ε t > 0 and ε t|t > 0 for every t ∈ T (denote such a collection

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(n/(n +1))(1/(n + 1) + 1/2). Hence, under the BD-D and the DB-B processes, even for an infinite fitness r, the fixation of a mutant in a finite population is not guaran- teed. This case appears even in a homogeneous population of finite size under the DB-B process where the fixation **probability** of a single mutant tends to 1 − 1/(n +1) with the increase in r. This means that the concept of the parameter r representing fitness (the relative fitness of mutants and residents) is questionable. In its simplest definition, fitness can be thought of as the lifetime reproductive success of an indi- vidual. This is not straightforward to interpret on a finite graph where the population is kept fixed, but it should have some basic properties. We contend that an individual with 0 fitness should be certain to be eliminated and one with infinite fitness should be certain to fixate. From this point of view, the IP and VM processes are consistent, but the BD-D and DB-B processes are not. In these processes r might be thought of as a function of fitness, but not “fitness” as such.

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Our main interest, therefore, lies with the derivation of an uncoupled dynamics, which, on the one hand, explicitly considers mutation and, on the other hand, is as close as possible to standard RD, and with the analysis of how this mutation mechanism affects the position and stability of equilibria compared to the standard (multi-population) RD. The resulting mutation mechanism with spontaneous mutations from one type to another is of course not appropriate for all biological mutation processes. In a biological population, such spontaneous mutation between a finite number of types occurs, e.g., for single nucleotide polymorphisms, where alleles differ by only one nucleotide, with the number of possible single nucleotide polymorphisms at that position restricted to four. Furthermore, such point mutations are known to occur with a non-negligible **probability** [31,32] and can be significant factors in diseases, [32,33], e.g., sickle cell anaemia, [34,35], which also interacts with malaria parasites, [36], cystic fibrosis, [37], or β thalassemia, [38,39], and further in human cancer cells, [40,41]. There is further evidence that in Drosophila most such nonsynonymous point mutations are deleterious, while the rest are slightly deleterious, near-neutral, or weakly beneficial, [42], suggesting that a weak selection assumption as we employ can be reasonable for persisting polymorphisms. Considered as a learning dynamics, modifications of multi-population RD have been shown to be linked to so- called Q-learning, a more sophisticated reinforcement learning algorithm, [43]. In particular, the resulting modification can be interpreted as a mutation-like term.

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while the professor would naturally like his salary to be as high as possible. The dean, knowing that similar professors’ salaries range between, say, 0 and 120, asks the professor if he can provide some evidence of his “value” (such as whether a recent paper was accepted or rejected, outside offers, and so on). Assume that with **probability** 50% the professor has no such evidence, in which case his expected value is 60, and with **probability** 50% he does have some evidence. In the latter case it is equally likely that the evidence is positive or negative, which translates into an expected value of 90 and 30, respectively. Thus there are three professor types: the “no-evidence” type t 0 , with **probability** 50% and value 60, the “positive-evidence” type t + , with

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to provide paraphrasing **probability** as a reward. Since paraphrasing is more about semantic sim- ilarity than superficial word/phrase matching, it treats question paraphrases more fairly (Example 1 in Table 2). Therefore, we first train a QPC model with Quora Question Pairs dataset. Next, we take it as an environment, and the QG model will interact with it during training to get the prob- ability of the generated question and the ground- **truth** question being paraphrases as the reward. QAP Reward Two observations motivate us to introduce QAP reward. First, in a paragraph, usu- ally, there are several facts relating to the an- swer and can be used to ask questions. Neither the teacher forcing or the QPP reward can favor this kind of novel generation (Example 2 in Ta- ble 2). Second, we find semantically-drifted ques- tions are usually unanswerable by the given an- swer. Therefore, inspired by the dual learning al- gorithm (He et al., 2016), we propose to take the **probability** that a pre-trained QA model can cor- rectly answer the generated question as a reward, i.e., p(a ∗ |q s ; p), where a ∗ is the ground-**truth** an-

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have drawbacks. However, the literature on game theory and semantics has in- dicated that a variation that is less rationally demanding is welcome in at least the study of linguistics. The relationship, or bridge law, between information, preferences and actions is preserved in **evolutionary** game theory, but it is not “rationality” in the philosophical sense. In fact, it has been claimed many times in this thesis that in **evolutionary** game theory, strategies are reinterpreted as an expression of a gene. If this is true, then we can claim that the “space” between the player, his actions and preferences just disappears, as if the rela- tionship replacing rationality is equality. If this is the case, may motivate us to let go of rationality as necessary component of game theory, for under the group dynamics setting of **evolutionary** game theory, we get the same result. If not a player is not“rational”, then he cannot “exist”. This suggests that there is I stated above that I would not claim that game theory should be void of a bridge law; what I claim is that one acceptable form of “bridge law” is by means of collapsing strategy and player into one term. The system is not void of a bridge law, but the concepts being bridged became one, also eliminating the need for a bridge law altogether. By doing this, we can also adjust the standard notion of preference to fit this **evolutionary** interpretation. The next section will fully describe an appealing logic where strategy and player become one formal term.

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In this paper, we introduced the literature of PBIL-based learning of Bayesian network models, and proposed a new mutation operator called **probability** mutation that manipulates **probability** vector of PBIL. Through evaluation of these algorithms, we found that (i) the PBIL-based algorithm outperforms K2-based traditional algorithms with the long- term continuous improvement, and (ii) **probability** mutation works well under PBIL-based algorithms especially in long- term computation to obtain high-quality Bayesian network models. Designing more efficient search algorithms based on EDA is one of the most attractive future tasks.

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Since, historically, games involving chance brought about the development of probability theory, it has been suggested that games of chance could profitably be used in the classroom to h[r]

Condensation phenomena arise through a collective behaviour of particles. They are ob- served in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra- cold bosonic gases (Bose-Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth-death processes, which also occur in **evolutionary** game theory. Here, we apply concepts from **evolutionary** game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may os- cillate, as we demonstrate for a rock-paper-scissors game of condensates.

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ysed a collection of CDs which provide metadata about the tuning system, and found that while this information is mostly correct, there were several cases in which another tempera- ment matches the data more closely than the advertised one. This is perhaps more surprising to a music theorist than to a practising tuner or performer, reflecting the dichotomy be- tween those who see temperament as a mathematical system and those who have to retune their instrument during the in- terval of a concert. This also raises an interesting issue about the nature of human annotations and their use as “ground **truth**”. The metadata provided with the CD is intended to give an indication of the tuning system rather than scientifi- cally accurate documentation, and we need to be discerning in the use of metadata that has been collected for a purpose other than scientific analysis or evaluation.

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and Brekelear in 1998 which was faster than Theobald’s method [11]. Binary decision diagram is used in [12] in order to design multi-level hazard free circuit considering MIC by unbounded gate and wire delay model assumption. Synchronous technology mapping technique is used to design generalized fundamental mode asynchronous circuit [13]. All above approaches suffer from some disadvantages and constraints like bounded wire and gate delay model, two phase algorithm, dedicated hazard free algorithm and demand to synchronous technology mapping tool. Consequently this paper proposes an **evolutionary** algorithm based design which doesn’t suffer from such a problem. This paper is organized as follows. Section 2 provides brief introduction to hazard, delay models and applied hazard detection technique. In section 3 applied **evolutionary** algorithm is described. Experimental result is presented at section 4. Finally proposed method is concluded in section 5.

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To see why these strategies are payoff dominant in CS **games**, consider that the best strategies in CS **games** will minimize the average distance between state and act thereby maximizing payoff. Given a sender strategy for any particular signal, the receiver can minimize average distance by playing the act that is appropriate for the median of the states associated with that signal. Given this type of best response on the part of the receiver, the sender then minimizes distance by using signals for only convex groups of states, and making those groups as small as possible, i.e., splitting the state space equally or nearly equally depending on the number of states. 10 These facts about the payoff dominant Nash equilibria of CS **games** not only mean that the number of equilibria is reduced in these **games**, but that the best equilibria are reduced whenever states outnumber signals. Furthermore, the larger the CS game, and the smaller the number of signals, the more significant the reduction in equilibria. This occurs because larger **games** have proportionately fewer equilibrium strategies where signal assignment is convex, etc. As will become clear in the next section, equilibrium selection in **evolutionary** models of these **games** seems to be eased by these reductions in equilibria.

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