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Figure from:Reconciling Normative and Behavioural Economics

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the payoffs in the last 4 cells are not determinate and depend on the strategy chosen by the players from each population (the 4 vectors of payoff are possible, since both strategies are rationalisable for both players). There exist 4+ = 256 pos- sible heuristics subgames, according to whether each type CD and DC from each population cooperates or defects with CD and DC types from the other population. We can then notice that, in the different subgames, only two pure strategy Nash equilibria are possible: {DD; DD} (for any subgame) and {CD;CD} (in the sub- games in which CD cooperates with CD, and either DC cooperates with CD or CD defects with DC). PMB is therefore as-if evolutionary stable in the replicator dynamics described in Consider now the PD discussed above: in section 7.2, we explicitly excluded the possible cases for which there was not a unique equilibrium for a given set of reply unctions. We can now also treat the cases of equilibrium non-uniqueness. Recall that 4 reply functions in pure strategies are available to the players, CC, DD, CD and DC. The problematic cases concerns the interaction of CD and DC types: when two CD or two DC met, there exist two pure strategy Nash equilibria, whereas the interaction of a CD type with a DC type does not have any pure strategy equilibrium. n all cases we can however notice that we have for both players C;(R) = {C; D}, ice. that they can all rationalise the choice of one of the two available pure strategies. The general payoff matrix for each heuristics subgame is the following: The general payoff matrix for each heuristics subgame is the following: — Table 2 the payoffs in the last 4 cells are not determinate and depend on the strategy chosen by the players from each population (the 4 vectors of payoff are possible, since both strategies are rationalisable for both players). There exist 4+ = 256 pos- sible heuristics subgames, according to whether each type CD and DC from each population cooperates or defects with CD and DC types from the other population. We can then notice that, in the different subgames, only two pure strategy Nash equilibria are possible: {DD; DD} (for any subgame) and {CD;CD} (in the sub- games in which CD cooperates with CD, and either DC cooperates with CD or CD defects with DC). PMB is therefore as-if evolutionary stable in the replicator dynamics described in Consider now the PD discussed above: in section 7.2, we explicitly excluded the possible cases for which there was not a unique equilibrium for a given set of reply unctions. We can now also treat the cases of equilibrium non-uniqueness. Recall that 4 reply functions in pure strategies are available to the players, CC, DD, CD and DC. The problematic cases concerns the interaction of CD and DC types: when two CD or two DC met, there exist two pure strategy Nash equilibria, whereas the interaction of a CD type with a DC type does not have any pure strategy equilibrium. n all cases we can however notice that we have for both players C;(R) = {C; D}, ice. that they can all rationalise the choice of one of the two available pure strategies. The general payoff matrix for each heuristics subgame is the following: The general payoff matrix for each heuristics subgame is the following:

Related Figures (12)

Abstract: This chapter investigates the historical origins of the model of the inner rational agent. We suggest that the two main arguments justifying the notion of true preferences are grounded on two quite different conceptions of the ‘economic man’, one as the simplification of a real individual and another as a representative agent. We show that this duality finds its origins within the marginalist revolution: while Jevons and Menger considered economics as a science of individual choice, Walras and later Marshall considered it as a science of social institutions. These two specific methodological approaches generated two distinct figures of the economic man, and we suggest that the current ambiguity about the nature of the neoclassical economic man results from the homogenisation of those two approaches through Pareto’s definition of the Homo economicus. We are then able to question the relevance of assuming that individuals present true preferences, since the coherence of those Abstract: This chapter investigates the historical origins of the model of the inner How we Became Rational: the Duality of the Economic Man

Abstract: we develop in this chapter a model of preference formation, that will Abstract: we d evelop in this chapter a model of preference tormation, that will constitute the basis of the general model of preferences we will present in chapter 6. We assume t hat the players are able to choose in a precommitment game the weights they assign to the other players’ material payoff in their own preferences, and determine t he optimal weights each player should choose so as to maximise her material payoff. We highlight a systematic relation between supermodularity (submodularity) and the formation of cooperative (competitive) preferences. We then investigate the possible implications of this framework for the design of public policies. We show in the case of climate change negotiations that international agree- ments relying on technology standards with trade sanctions rather than objectives

Chapter 5. Choosing One’s Preferences Lemma 1 provides the expression of the first order derivative of the Stackelberg best reply function f;(x;) as a function of the second order derivatives ie . We can then show that the sign of Oh is the same than Ut" (z(3)|5), when conditions (i) and (ii) are verified (lemma 2). Condition (i) means that j’s impact on 7’s marginal utility is relatively low compared to 7’s impact on her own marginal utility (this is a strong form of row diagonal dominance), and (ii) the cross derivatives oh and Ue are relatively ‘close’ in absolute value Vj, k 4 i, i.e. there is no player 7 with a significantly higher importance from i’s perspective. Those conditions are typically U;7 states that, under the same conditions, the sum of the (i;7) cofactors, Vj 4 i, is verified for public good games and two-player games with |U#| > . Lemma 3 lower than the principal minor of J(S$).

with R> P> 0. If R = P, the game is a pure-coordination game, and game the- ory cannot predict which equilibrium the players should choose. Several empirical studies however show that real individuals successfully exploit apparently irrelevant features of the choice environment to determine their choice (Schelling, 1960, Mehta et al., 1994a,b, Bacharach and Bernasconi, 1997), such as the lexicographical order of the strategies in the above example (‘A’ indeed appears to be more salient than ‘B’, and actual players may therefore be tempted to play A because they expect the others to recognise A as a salient strategy too). ore strikingly, if R > P, we are in presence of a Hi-Lo game, in which one equi- red . TY oT 7 . a a7 a7 A V,7 1 a7 1 . a 1 . 1 The second puzzle of game theory is the issue of equilibrium selection in coordi

A difficulty of this kind of approach is the interpretation we should give to such ‘social preferences’: it is indeed unclear whether those preferences are immutable, i.e. whether cooperating in a social dilemma truly reflects empathetic concerns for other humans (such as inequity aversion) or simply reflects the compliance to what the individual think is t (2009), Binmore (2010) and t that cooperative be haviours oO concern for fairness, and that social preferences, t hen two p inequity not uniquely in socia other games. Consid he social norm in the game (see for instance Gintis he discussion between Binmore and Shaked (2010), Eckel and Gintis (2010) and Fehr and Schmidt (2010)). For instance, if we assume bserved in experiments highlight the existence of a individuals are instrumentally rational given their ayers, both averse to inequity, should be averse to dilemmas. Their concern should remain stable for er for instance the two following games: other games. Consider for instance the two following games: G2 is a similar situation in which the payoffs have been inverted. In this case, there

In the transformed PD, {C;C} constitutes now a second Nash equilibrium explaining the coexistence of cooperative and non cooperative behaviours in socia dilemmas. However, although inequity aversion seems to offer a relevant theory of unselfish behaviour, it also implies a quite odd result in the second game G2’ we find indeed that {D; D} is now also a Nash equilibrium, which is here Paretc dominated. If the players are concerned by inequity, then we should also finc empirical evidence of individuals playing the strategy D in G2, although this strategy is strictly dominated and lead to a suboptimal equilibrium. If we accept inequity aversion as the explanation of cooperation in the PD, we should als« expect finding puzzling predictions in games like G2. Explaining unselfish behaviours by altering individual preferences should als« In the transformed PD, {C;C} constitutes now a second Nash equilibrium, Chapter 6. The Rationale of Team Reasoning

As an illustration, consider the two games G1 and G2 discussed above: Suppose that P1 and P2 are team reasoners, and that this is common knowledge.

Suppose also for convenience that the preferences of N are such that the vector nature. The games can therefore be represented as follows:

So as to illustrate Bacharach’s notion of ‘frame’, consider the following Rubin vase: There are two main representations of this object: we can either perceive two There are two main representations of this object: we can either perceive two black faces on a white background, or a white vase on a black background. An interesting property of ambiguous images such as the Rubin vase is that we cannot perceive simultaneously the faces and the vase, although we may know that both perceptions are possible. This means in particular that there is no ‘good’ perception of the object: the two perceptions in terms of faces and vase are both equally valid perceptions. Within the framework of variable frame theory, it is assumed that there exists an object that is beyond human perception, which determines our possible perceptions of it®. The observer has then two main ways of framing this object: either as ‘two faces’ or as ‘one vase’. model the process of selection of frames. He informally suggests the ‘interdependence hypothesis’ as an explanation of the emergence of team reasoning. In a nutshell, this hypothesis states that, if an outcome that can be reached by an individually rational reasoning is Pareto dominated by an outcome that can only be reached by a collective reasoning (such that the cooperative outcome in a PD), then group identification and the selection of a we-frame is more likely (Smerilli, 2012). Bacharach (2006) also provided arguments to justify from an evolutionary perspective the selection of frames: while I-frames will be more successful at the individual level, we-frames will favour groups of players whose proportion of team reasoners is higher. This combination of individual and group selection (multilevel selection theory, see Sober and Wilson (1998) for a presentation) implies that, although the share of team reasoners tends to decrease within each group over time, the groups with a high share of team reasoners tend to grow faster, while non cooperative groups progressively disappear: it is therefore possible that the share of team reasoners in the total population eventually increases. Qn age tr ilretrate Rarharach’e nntinn nf ‘frame’ ennedar thea fallagringe Riuhin waca:

Abstract: We provide in this chapter a justification of team reasoning as an ecolog- ically rational heuristic. We slightly amend the indirect evolutionary approach — by suggesting studying the evolution of individual heuristics rather than individual preferences — and study the evolutionary stability of payoff maximising behaviour in finite games. We define the strict ¢-core as a refinement of the y-core by as- suming that the deviating coalition acts as a Stackelberg leader and the remaining individuals as singletons. We show that maximising one’s payoff is evolutionary stable if and only if the resulting Nash equilibrium belongs to the strict ¢-core. We can then highlight that, when the players use the heuristics that outperform payoff

Without loss of generality, suppose that Gy is positive (which is true if n is odd). We therefore have: We now show that, under the same assumptions than lemma 2, we have

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