Hyperbolic Discounting can represent Consistent Preferences

Among non Exponential Discounting (ED) models, introduced to capture time inconsistent choices, Hyperbolic Discounting (HD) recently gained particular relevance. This paper points out that, for some particular payoff structures, HD can also represent consistent preferencesTime Consistency, Hyperbolic Discounting

Cooperation with Strategy-Dependent Uncertainty Attitude

The paper shows that in a Prisoner’s Dilemma Knightian uncertainty, formalised by multiple priors, may entail cooperation at a generalised Nash Equilibrium. The main idea is that players may have an attitude towards uncertainty that depends upon their available strategies. In particular, if players anticipate to be sufficiently more optimistic when choosing to cooperate, than when defecting, then they may indeed cooperate. Though uncommon in economic modelling, choice-dependent uncertainty attitude formalises a behaviour which is well understood and widely accepted by cognitive psychologists, within the theory of Cognitive Dissonance.Cooperation, Cognitive Dissonance, Equilibrium, Games, Uncertainty

Dynamic Consistency in Extensive form Decision Problems

In a stimulating paper Piccione and Rubinstein (1997) argued how a decision maker could undertake dynamically inconsistent choices when, in an extensive form decision problem, she exhibits a particular type of imperfect recall named absentmindedness. Such imperfection obtains whenever an information set includes histories along the same decision path. Starting from work focusing on the Absentminded Driver example, and independently developed by Segal (2000) and Dimitri (1999), the main theorem of this paper provides a general result of dynamically consistent choices, valid for a large class of finite extensive form decision problems without nature.

Liquid Proof-of-Stake in Tezos: An Economic Analysis

n this paper, we investigate some economic fundamentals related to the Tezos blockchain platform under the Emmy* consensus protocol. The protocol is based on a liquid version of Proof-of-Stake, in the sense that users can temporarily delegate some or all of their Tz units to full nodes. In addition to increasing the stake of the full node, and thus the probability of being selected as a block baker/endorser, such delegation induces the property of the super-additivity of users’ selection probability of baking/endorsing a block. That is, with delegation, the selection probability may be larger than the sum of the selection probabilities without delegation. In this paper, we study how monetary holdings and stakes can evolve with time, also discussing the individual user and the market implications of delegation

Hyperbolic Discounting can Represent Consistent Preferences

Among non Exponential Discounting (ED) models, introduced to capture time inconsistent choices, Hyperbolic Discounting (HD) recently gained particular relevance. This paper points out that, for some particular payoff structures, HD can also represent consistent preference

Pricing cloud IaaS computing services

Abstract The economics of cloud computing has recently attracted increasing attention. In particular, a topic which is still under debate is how prices charged to customers for cloud resources are formed, since alternative pricing rules could be considered. Based on three pricing schemes inspired by those used by Amazon EC2, the main global cloud service provider, in the paper we address two main issues. First we present a methodology for the relevant parameters of the pricing rules to be determined in an optimal way, that is to maximise the provider's revenue. Moreover, we discuss reasons for co-existence of three pricing rules, rather than fewer, to access the cloud. Our findings suggest that this may be due to a larger coverage of the potential demand, since customers applying for cloud services vary in their willingness to pay for the job, the time length of the service, the computational power requested etc. Furthermore, the pricing rule in the so-called, spot market, can provide the platform with useful information on the customers willingness to pay for cloud services. This is because in the spot market users offer a price for service, but pay less than that if their request is satisfied

Bitcoin mining as a contest

This paper presents a simple game theoretic framework, assuming complete information, to model Bitcoin mining activity. It does so by formalizing the activity as an all-pay contest: a competition where participants contend with each other to win a prize by investing in computational power, and victory is probabilistic. With at least two active miners, the unique pure strategy Nash equilibrium of the game suggests the following interesting insights on the motivation for being a miner: while the optimal amount of energy consumption depends also on the reward for solving the puzzle, as long as the reward is positive the decision to be an active miner depends only on the mining costs. Moreover, the intrinsic structure of the mining activity seems to prevent the formation of a monopoly, because in an equilibrium with two miners, both of them will have positive expected profits for any level of the opponent's costs. A monopoly could only form if the rate of return on investment were higher outside bitcoin

A Characterisation of verifiability and observability in contracts

Reference to the notions of verifiability and observability is widespread in contract theory. This paper is a contribution towards a formalization, and related characterizations, of these two notions. In particular we first define them, through knowledge operators, and then provide characterization results in terms of the relevant state spaces. Since, when referring to a contract, observability typically pertains to parties while verifiability to the court, we define them differently. A main finding of the paper is that for proper contract verifiability to obtain the court must imagine true states and have information processing abilities as good as the parties

Transaction Fees, Block Size Limit and Auctions in Bitcoin

Confirmation of Bitcoin transactions is executed in blocks, which are then stored in the Blockchain. As compared to the number of transactions in the mempool, the set of transactions which are verified but not yet confirmed, available space for inclusion in a block is typically limited. For this reason, successful miners can only process a subset of such transactions, and users compete with each other to enter the next block by offering confirmation fees. Assuming that successful miners pursue revenue maximization, they will include in the block those mempool transactions that maximize earnings from related fees. In the paper we model transaction fees as a Nash Equilibrium outcome of an auction game with complete information. In the game the successful miner acts as an auctioneer selling block space, and users bid for shares of such space to confirm their transactions. Moreover, based on expected fees we also discuss what the optimal, revenue maximizing, block size limit should be for the successful miner. Consistently with the intuition, the optimal block size limit resolves the trade-off between including additional transactions (which possibly lower the unit fees collected) and keeping the block capacity limited (with, however, higher unit fees)

Gains and losses in intertemporal preferences: a behavioural study

According to recent evidence (Frederick, Loewenstein, & O’Donoghue, 2002), the traditional Discounted Utility model (Samuelson, 1937) has a limited ability to describe realistic models of behaviour and indeed there are several documented empirical regularities that seem to contradict this statement both in certainty and uncertainty conditions. This study focused on one of the best documented anomalies: sign effect or gain-loss asymmetry (Frederick et al., 2002; Loewenstein & Prelec, 1992; Read, 2004). Specifically, the study investigated the intertemporal preference for symmetric monetary rewards and punishments in certain conditions, and the no wealth effects hypothesis (Dimitri, 2007) by asking subjects to choose between two positive or two negative euro amounts available at different points in time. The experimental design applied here followed the same behavioural pattern of the neuroeconomics’ study on monetary rewards realized by McClure et al. (2004). The results confirmed a gain-loss asymmetry at least for medium and large euro amount and suggested new directions of research.intertemporal preferences; gains; losses; certainty; sign effect .