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Theory 2: Simultaneous Games Therefore bar A will serve 4000 beers to spasms near temple order rumalaya gel no prescription the natives yellow muscle relaxant 563 purchase rumalaya gel 30 gr overnight delivery, and 3000 beers to muscle relaxant india cheap rumalaya gel 30 gr line tourists, serving 7000 beers in total, making 7000 2 D 14000 dollars. The payoff matrix, with values in thousands of dollars, is 2 4 5 2 10, 10 12, 14 15, 14 4 14, 12 20, 20 15, 28 5 14,15 28, 15 25, 25 For each bar, move "4" strictly dominates move "2", therefore we could eliminate both moves "2" to get the reduced game: 4 5 4 20, 20 15, 28 5 28, 15 25, 25 Now, but not before the elimination, move "4" strictly dominates move "5". Therefore we eliminate these moves for both players as well and arrive at a game with only one option, "4", for each player, and a payoff of \$ 20000 for each. So the weakly dominating move is never worse than the weakly dominated one, and sometimes it is better. This opinion is also based on different behavior of Nash equilibria (discussed in Section 2. Your friend has been thinking about her move, arrives on a decision what move to play, and writes it on a piece of paper so as not to forget it. The move you play under these conditions is called the best response to the move of your friend. The label of the corresponding column is the best response to the move corresponding to that row. The label of the corresponding row is the corresponding best response for the move corresponding to that column. Assume Ann has four moves, A1, A2, A3, A4, and Beth has three B1, B2, and B3. Best Response for Three Players Best responses make also sense for games with three or more players. Here we look at first entries only, and compare cells having the same position in the different matrices, as "upper left", for instance. For the second matrix, the highest third entry in the first row is 1, and in the second row 0. An outcome is called a pure Nash equilibrium provided nobody can gain a higher payoff by deviating from the move, when all other players stick to their choices. A higher payoff for a player may be possible, but only if two or more players change their moves. Theory 2: Simultaneous Games Nash equilibrium if each move involved is the best response to the other moves. A cell in the normal form is a pure Nash equilibrium if each entry is marked (underlined in our examples) as being the best response to the other moves. If some (non-binding) negotiation has taken place before the game is played, each player does best (assuming that the other players stick to the agreement) to play the negotiated move. The police have little evidence, and if both remain silent they will be sentenced to one year on a minor charge. Therefore the police interrogators propose a deal: if one confesses while the other remains silent, the one confessing goes free while the other is sentenced to three years. Furthermore, the best response to move S is C, and the best response to move C is also move C, therefore the pair (C, C)-both confessing forms the unique Nash equilibrium of this game. The choice C -confessing-with payoffs of only 1 may seem counterintuitive if negotiations can take place in advance, but their terms are non-binding and cannot be enforced. It would be useless to agree on move S in advance, since each of the players would feel a strong urge to deviate (cheat). Only if binding agreements are possible, would both agree on the S -S combination, reaching a higher payoff. Each person likes to do something together with the other, but the man prefers soccer, and the woman prefers ballet. To simplify the game, we assume that the total payoff for each player is the sum of the payoffs (in terms of satisfaction) of being at the preferred place, which gives a satisfaction of c satisfaction units, and 2. Which Option to Choose 11 being together with the partner, giving d satisfaction units. We have two variants, depending on whether c or d is larger, the low or high love variants. The assumption of the additivity of satisfaction is severe-satisfaction could just as well be multiplicative, or some more complicated function of c and d. It could even be that satisfaction in one area could interfere with satisfaction in the other. The satisfactions may differ for both persons, one appreciating the presence of the other more than the other, or one having a clear preference for soccer or ballet, when the other is indifferent.

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Reflective Listening is used to muscle relaxant options discount rumalaya gel uk clarify what is being said and convey mutual understanding spasms meaning purchase rumalaya gel uk. However muscle relaxant on cns rumalaya gel 30 gr mastercard, this does not mean simply parroting back to the person what they have just said. It is most applicable when someone talks to you in an emotional way, such as when they are unhappy, angry, happy, sad, etc. Generally, when people display these emotions, a subconscious desire exists for those emotions to be recognized and acknowledged by others. By reflecting those feelings back to them, you are acknowledging them and demonstrating that you care how they feel. Examples include: "You seem to be in a good mood today" or "it seems that really upset you. Desire to explore a problem and help the other party understand the dimensions of the problem, possible choices, and their consequences. A reflective response lets you communicate to a person what you perceive they are doing, feeling, and saying. It is clearly impossible to be the other person and your best understanding is only a reasonable approximation. However, despite its limitations, this approach helps you be open-minded and not be quick to judge. Reflective listening, as effective as it is, is not intended to be used at all times and in every situation, which is neither practical nor helpful. Those times when it is beneficial include: When the other person has a problem and needs a sounding board to sort through it. When you are in a meeting and feel you must disagree or challenge what someone has said. When you are in a meeting and want to verify that you understand what someone has stated. One way to improve your listening is to take notes on what the other person is saying. This obviously is not recommended for a casual conversation, but can be effective in meetings, speeches, presentations, etc. However, when you concentrate on taking notes, you tend to hear only half of what is being said. You should write down just enough to let you recall David Kolzow 134 the key ideas. In summary, effective listening skills can be acquired by doing the following simple steps: 156 Step 1: Face the speaker and maintain eye contact. Talking to someone while they scan the room, study a computer screen, or gaze out the window is like trying to have a conversation with your cat. In most Western cultures, eye contact is considered important to effective communication. However, keep in mind that in some cultures it is very impolite and even an insult to look someone in the eye. To aid in being attentive, it is helpful to mentally screen out distractions, like background activity and noise. Listen without judging the other person or mentally criticizing the things he/she tells you. If what is being said makes you uncomfortable, it is Dianne Schilling, "Ten Steps to Effective Listening. One should also listen without jumping to conclusions and anticipating what a person is trying to say. Remember that the speaker is using language to represent the thoughts and feelings inside his/her mind. Allow your mind to create a mental model or picture of the information being communicated.

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If one of the terms happens to muscle relaxant for stiff neck safe rumalaya gel 30 gr be an existential spasms in 7 month old buy rumalaya gel in united states online, then it will be replaced everywhere with the other term spasms vitamin deficiency purchase rumalaya gel in united states online. We check the proof only for its unification side effects, ignoring the associated variable dummy. This technique is even more useful within recursive and iterative tactics that are meant to solve broad classes of goals. We will write, in Gallina, decision procedures with proofs of correctness, and we will appeal to these procedures in writing very short proofs. The term reflection applies because we will need to translate Gallina propositions into values of inductive types representing syntax, so that Gallina programs may analyze them, and translating such a term back to the original form is called reflecting it. The Ltac-programming techniques that we learned in the last chapter make it easy to implement such a procedure. This procedure always works (at least on machines with infinite resources), but it has a serious drawback, which we see when we print the proof it generates that 256 is even. Sometimes apparently large proof terms have enough internal sharing that they take up less memory than we expect, but one avoids having to reason about such sharing by ensuring that the size of a sharing-free version of a term is low enough. Superlinear evenness proof terms seem like a shame, since we could write a trivial and trustworthy program to verify evenness of constants. It is also unfortunate not to have static typing guarantees that our tactic always behaves appropriately. Other invocations of similar tactics might fail with dynamic type errors, and we would not know about the bugs behind these errors until we happened to attempt to prove complex enough goals. We will be able to write proofs like in the example above with constant size overhead beyond the size of the input, and we will do it with verified decision procedures written in Gallina. For this example, we begin by using a type from the MoreSpecif module (included in the book source) to write a certified evenness checker. Inductive partial (P: Prop): Set:= Proved: P [P] Uncertain: [P] A partial P value is an optional proof of P. These overlap with some of the notations we have seen previously for specification types, so they were placed in a separate scope that needs separate opening. The function check even may be viewed as a verified decision procedure, because its type guarantees that it never returns Yes for inputs that are not even. When given a partial P, this function partialOut returns a proof of P if the partial value contains a proof, and it returns a (useless) proof of True otherwise. Definition partialOut (P: Prop) (x: [P]):= match x return (match x with Proved P Uncertain True end) with Proved pf pf Uncertain I end. However, it turns out to be very useful in writing a reflective version of our earlier prove even tactic: Ltac prove even reflective:= match goal with [isEven We identify which natural number we are considering, and we "prove" its evenness by pulling the proof out of the appropriate check even call. Recall that the exact tactic proves a proposition P when given a proof term of precisely type P. The size of the proof term is now linear in the number being checked, containing two repetitions of the unary form of that number, one of which is hidden above within the implicit argument to partialOut. If we reduced the first term ourselves, we would see that check even 255 reduces to a No, so that the first term is equivalent to True, which certainly does not unify with isEven 255. Our tactic prove even reflective is reflective because it performs a proof search process (a trivial one, in this case) wholly within Gallina, where the only use of Ltac is to translate a goal into an appropriate use of check even. For large formulas, this can add a linear amount of proof size overhead, beyond the size of the input. To write a reflective procedure for this class of goals, we will need to get into the actual "reflection" part of "proof by reflection. This inductive type is a good candidate: Inductive taut: Set:= TautTrue: taut TautAnd: taut taut taut TautOr: taut taut taut TautImp: taut taut taut. Such functions are also called interpretation functions, and we have used them in previous examples to give semantics to small programming languages. Fixpoint tautDenote (t: taut): Prop:= match t with TautTrue True TautAnd t1 t2 tautDenote t1 tautDenote t2 TautOr t1 t2 tautDenote t1 tautDenote t2 TautImp t1 t2 tautDenote t1 tautDenote t2 end. To use tautTrue to prove particular formulas, we need to implement the syntax reification process.