analytical evaluation of lead time demand in polytree supply chains with uncertain demand lead time and inter demand time abstract in a stochastic supply chain network knowing the exact distribution of lead time demand ltd for each node allows determining inventory policy parameters service levels and optimal costs to determine the ltd distributions a stochastic analytical model has been developed for a multi echelon supply chain organised into an arbitrary polytree network where the variables demand quantity lead time and inter demand time are uncertain and can follow any probability distribution the model is based on a conventional nq batch policy for each node with discrete time and continuous demand any network can be broken down into four basic elements which represent root and leaf node topologies the model derives key convolutions for the four basic elements and then follows the same technique for evaluating resulting ltd distributions for each node in the network the paper presents the formulation in seven steps that can be used to obtain exact ltd distributions either in the two dimensional form or as a compound one dimensional ltd distribution per variable lead time for each node in any polytree supply chain the ltd distributions can be calculated either analytically for smaller networks or using numerical integration for larger networks the validation of the developed framework has been conducted by comparing the obtained formalism based ltd distribution for two test networks against simulation the pairs of simulated and formalism based distributions have been plotted against each other as well as subjected to various goodness of fit tests and error analysis the results suggest that the formalism based and simulated probability distributions are consistent

estimating the lead time demand distribution when the daily demand is non normal and autocorrelated hon shiang lau abstract this paper develops convenient formulas for estimating the probability distribution of lead time demand when the inventory item s daily demand follows a probability distribution of any arbitrary shape and when simple univariate models can be found for the autocorrelated daily demand series numerical examples are presented to illustrate the use of these formulas the numerical results also indicate that significant error may be incurred when inventory decisions are made without proper consideration of the autocorrelations or the arbitrary distribution shapes of daily demands

long run competition in capacity short run competition in price and the cournot model in this article we investigate the nature of equilibrium in markets in which firms choose the scale of operation before they make pricing decisions we analyze a duopoly model in which firms choose their capacities before engaging in bertrand like price competition we demonstrate that the cournot outcome is unlikely to emerge in such markets and that the equilibrium tends to be more competitive than the cournot model would predict in addition our results indicate a tendency toward asymmetric firm sizes and price dispersion that results from the mixed strategies firms use in equilibrium

sunk costs and strategic commitment a proposed three stage equilibrium dixit s i980 paper in this journal the role of investment in entry deterrence has attracted considerable interest from economists concerned with constructing a modern theory of strategic behaviour towards entry in fact the paper has spawned quite an industry of commitment models in which the equilibrium payoffs in some final period game can be influenced by strategic commitments made by the players in an earlier period for similar models with important insights into strategic entry deterrence see eaton and lipsey i980 i98i schmalensee i98i the purpose of this note is to argue that when the instrument of stragetic commitment takes the form of sunk costs which both entrant and incumbent have to bear as it does in dixit s paper and in many other examples a three stage model rather than the two stage model presented by dixit is required although the proposed equilibrium differs from dixit s its qualitative features are the same it may or may not be profitable to deter entry and if it is the first mover may still prefer to play an accommodation strategy and allow entry to take place following dixit we restrict our attention to the asymmetric case in which one firm the incumbent makes the first move the two stage game involves the first mover sinking part of its costs in advance so that in the second stage equilibrium it will have a current cost advantage over the entrant which must incur the full cost of producing any desired output level the second period cost asymmetry ensures the incumbent a lar ger share of the post entry market which may be sufficient to deter entry altogether the problem with the two stage game lies in the nature of sunk costs sunk costs by definition are committed before the production period takes place if they were expended as a flow simultaneously with production they would not be sunk the installation of capacity is the natural example employed by dixit and well illustrates the point if installed capacity is a sunk cost which it must be for the incumbent to acquire any strategic advantage at all then the entrant s installed capacity is equally sunk and must also be committed before the production period takes place given this observation the post entry final period equilibrium should not be modelled as if the entrant were simultaneously incurring both variable and sunk costs but the incumbent only incurs variable costs this implies too great an asymmetry in favour of the incumbent the final period equilibrium should involve both firms incurring only variable

crowding out voluntary contributions to public goods we test the null hypothesis that involuntary transfers for the provision of a public good will completely crowd out voluntary transfers against the warm glow hypothesis that crowding out will be incomplete because individuals care about giving our design differs from the related design used by andreoni in considering two levels of the involuntary transfer and a wider range of contribution possibilities and in mixing groups every period instead of every four periods we analyse the data with careful attention to boundary effects we retain the null hypothesis of complete crowding out in two of three pairwise comparisions but reject it in favour of incomplete crowding out in the comparison most closely akin to andreoni s design thus we confirm the existence of incomplete crowding out in some environments but suggest that the warm glow hypothesis is inadequate in explaining it

evaluating the robustness of lead time demand models abstract this paper examines the robustness of lead time demand models for the continuous review r q inventory policy a number of classic distributions e g normal lognormal gamma poisson and negative binomial as well as distribution selection rules are examined under a wide variety of demand conditions first the models are compared to each other by assuming a known demand process and evaluating the errors associated with using a different model then the models are examined using a large sample of simulated demand conditions approximation results of inventory performance measures ready rate expected number of backorders and on hand inventory levels are reported results indicate that distribution selection rules have great potential for modeling the lead time demand

excess capacity and collusion in this paper the authors analyze a restricted class of equilibria in the dynamic model of j p benoit and v krishna 1987 in which firms choose their scale of operation before engaging in a repeated game of price competition benoit and krishna established that all firms carry excess capacity in all collusive equilibria as the authors are interested in the relationship between excess capacity and collusion in price they examine equilibria in which firms tacitly collude in price but not in investment decisions copyright 1990 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

the existence of equilibrium in discontinuous economic games ii applications in part i of this study we established two existence theorems for mixed strategy equilibrium in games with discontinuous payoff functions see theorems 4 4 and 5 5 in dasgupta and maskin 1986 hereafter d m 1986 in this second part we use the second of these two theorems to prove the existence of mixed strategy equilibrium in some wellknown discontinuous economic games that fail to have pure strategy equilibria the models we analyse are the bertrand edgeworth example of price setting duopolists with capacity constraints see section 2 2 price competition among firms producing differentiated products hotelling 1929 and d aspremont gabszewicz and thisse 1979 see section 2 3 spatial competition eaton and lipsey 1975 and shaked 1975 see section 3 and models of market dependent information rothschild and stiglitz 1976 and wilson 1977 section 4 the paper concludes section 5 with a classification of these models

a periodic review model with serially correlated inventory level dependent demand abstract it has been established that the demand rates of many consumer products are serially correlated and are dependent on the amount of inventory displayed to the customer a periodic review model is developed that considers both of these effects an adaptive base stock policy based on the critical fractile is presented and a solution methodology is developed the effect of this demand pattern on the safety stock requirement is investigated

non excludable public good experiments we conduct a two stage game experiment with a non excludable public good in the first stage two subjects choose simultaneously whether or not they commit to contributing nothing to provide a pure public good in the second stage knowing the other subject s commitment decision subjects who did not commit in the first stage choose contributions to the public good we found no support for the evolutionary stable strategy equilibrium and the ratio of subjects who did not commit to contributing nothing increased as periods advanced that is the free riding rate declined over time furthermore this behavior did not arise due to altruism or kindness among subjects but from spiteful behavior of subjects

transfers and the weakest link an extension of hirshleifer s analysis abstract with the weakest link social composition function analysed by hirshleifer it is shown that an incentive exists for some agents to transfer resources to others so as to achieve higher quantities of the public good the characteristics of such an equilibrium with transfers are examined together with the implications of differing income distributions for the quantity of the public good some observations are offered as to how well the model can capture co operative behaviour

the max min group contest weakest link group all pay auction we investigate a group all pay auction in which each group s effort is represented by the minimum among the effort levels exerted by the group members and the prize is a group specific public good we fully characterize the symmetric equilibria for two groups there are four types of equilibria the pure strategy equilibria in which all active players exert the same effort the semi pure strategy equilibria in which the players in a group play the same pure strategy whereas those in the other group play the same mixed strategy the nondegenerate mixed strategy equilibria with continuous support and the nondegenerate mixed strategy equilibria with discontinuous support we then analyze a general contest with n groups

price competition in a capacity constrained duopoly abstract this paper characterizes the set of nash equilibria in a model of price setting duopoly in which each firm has limited capacity and demand is continuous and decreasing in general there is a unique equilibrium so that comparative static exercises are meaningful the properties of the equilibrium conform with a number of stylized facts the equilibrium prices are lower the smaller is demand relative to capacity when demand is in an intermediate range the firms use mixed strategies they randomly hold sales if capacities are chosen simultaneously before prices the set of equilibrium capacities coincides with the set of cournot quantities

bertrand edgeworth duopoly with proportional residual demand a complete characterization is given for the prices charged by bertrand edgeworth duopolists with capacity constraints in general for the game in which firms strategy spaces consist of price offers nash equilibrium involves nondegenerate mixed strategi es equilibria never extend below the highest competitive price with tw o firms the bertrand edgeworth model displays a bias for the highest of several market clearing prices moreover these strategies never stop short of the lowest monopoly price if firms are of unequal siz e the larger firm assigns positive probability to a monopoly price possibly even to several monopoly prices copyright 1993 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

foreign aid and weakest link international public goods an experimental study in this paper we investigate efficiency differences between income and in kind transfers as distribution mechanisms of foreign aid to weakest link international public goods in a laboratory environment we find that if there is relatively small difference in country size then income transfers seem to provide a higher provision of the international public good and thus higher overall welfare level than that of in kind transfers however if there is a large disparity in country size then in kind transfers appear to provide a higher level of ipg provision and higher accompanying global welfare

weakest link public goods giving in kind or transferring money abstract this paper extends the analysis of weakest link public goods whose level equals the smallest of the agents provision levels by permitting an agent either to increase one s own provision or else augment both one s own provision and that of the other agent s nash equilibria may be either symmetric with agents matching one another s provision or else asymmetric with an in kind transfer by one agent to another an equilibrium with cash transfers but no in kind transfers may be pareto superior to one with only in kind transfers if agents differ in their efficiency then in kind transfers by the low cost agent may dominate a cash transfer the possibility of pareto improving transfers is enhanced as the number of agents increases

the existence of equilibrium in discontinuous economic games i theory the article presents information about the existence of equilibrium in discontinuous economic games in this paper and its sequel presents study the existence of nash equilibrium in games where agents payoff functions are discontinuous the enquiry is motivated by a number of recent studies that have uncovered serious existence problems in seemingly innocuous economic games in the sequel to this paper authors have explained the utility function in the economic games referred to earlier are neither continuous nor quasi concave however they demonstrate that the payoff functions in mildly modified versions of these constructs exhibit two weaker forms of continuity which together with the requirement of quasi concavity suffice for the existence of an equilibrium from this one may conclude that at least in the modified versions of these models discontinuities in the payoff functions are not the real source of the problem rather it is the failure of the payoff functions to the quasi concave which is responsible for the non existence of equilibrium these observations bear on the existence of nash equilibrium in pure strategies

safety stock determination with correlated demands and arbitrary lead times abstract in this new paper a new method is proposed for determining the safety stock when daily demands are autocorrelated and lead times follow an arbitrary distribution the method is then used as a basis for examining effects on the safety stock when the usual assumptions namely independence and normality of daily demand and normality of lead times are violated the new method is derived by using inequalities on the basis of probability arguments it is simple to use and provides an upper bound of the safety stock further numerical investigation based on the new method shows that the effect of autocorrelation is more pronounced than departure from normality in determining the safety stock substantial error may be incurred if such autocorrelation is ignored in the test cases

holding idle capacity to deter entry in this journal dixit i980 carefully analysed the extent to which an established firm facing a prospective entrant might make an investment in capacity beyond that which is optimal for its pre entry output in his model both the established firm and prospective entrants understand that a quantity setting nash equilibrium would be established in any post entry game dixit showed that spence i977 had studied an imperfect equilibrium that is an equilibrium that depended upon a threat that was not credible to obtain his result that firms might hold excess capacity to deter entry in a perfect equilibrium a firm would not wish to install capacity that would be left idle if entry did not occur dixit s conclusion however depends on his assumption that each firm s marginal revenue is always decreasing in the other s output this is quite a restrictive assumption for example it is never satisfied in the relevant range for economists second favourite demand curve constant elasticity demand the basic point is unchanged if the firms anticipate price competition with differentiated products rather thanquantity competition in any post entry game under quite plausible conditions rational firms facing rational potential entrants may install capacity that will certainly be left idle we are thus able to rehabilitate spence s original proposition in a perfect equilibrium setting

capacity output and sequential entry two crucial assumptions frequently made in industrial organization are that an established firm deters entry either by a constant high output the sylos postulate or by high excess capacity the excess capacity hypothesis these assumptions may be an accurate description of the observed conduct of firms in some industries however when the rules of the post entry game are clearly specified the optimal output and investment strategies of an established firm may depart considerably from these behavioral assumptions because of this possible inconsistency with rational behavior any conclusions about the formation of industry based upon either assumption are highly suspect what is more these assumptions avoid the main issue of whether entry deterrence is worthwhile at all this paper presents a dynamic model of entry in which established firms pursue a cournot nash alternatively stackelberg strategy toward a potential entrant the entrant behaves in cournot nash fashion and chooses output on the basis of expected postentry profits at the equilibrium of the post entry game within this framework a constant output entry deterring strategy would involve maintenance of an entry deterring output level before and after entry is threatened an excess capacity entry deterring strategy would involve holding excess capacity at an entry deterring level and increasing output to that level after entry is threatened special conditions are presented under which the sylos postulate or the excess capacity hypothesis will accurately describe optimal entry deterring strategies in addition special conditions are examined under which the established firm maintains a constant output or holds pre entry excess capacity when large scale entry does in fact take place the analysis shows that in general established firm reactions to entry are quite different from these special cases the sylos postulate see joseph bain paolo sylos labini franco modigliani 1958 asserts not only that potential entrants expect established firms to maintain their output constant as entry occurs but that established firms keep output constant at a level that deters entry whether or not it is profitable to do so hailed as a welcome major breakthrough on the oligopoly front modigliani 1958 the sylos postulate underlies many papers in the large theoretical and empirical literature on limit pricing yet the sylos postulate ignores both the strategic interaction between firms and the dynamic aspects of entry 2 unless the established firm s monopoly output exceeds the entrydeterring level the established firm with a general cost function able to choose an entry deterring output level will instead always desire a lower output level before entry for the special case where capacity is an upper bound on output and the established firm is a stackelberg leader in the post entry game

task divisions in teams with complementary tasks abstract a team leader and a team follower non cooperatively produce a team specific public good out of two complementary tasks both team members are identically productive and can contribute to both tasks by moving first the team leader effectively determines the division of the tasks in the team we show that the existence of multiple but finitely many types of task divisions is associated with a non convex leader s budget constraint non convexity generates discontinuities and non monotonicities in the equilibrium provision of the good and also in the follower s utility if incomes are redistributed within the team non monotonicity of the follower s utility motivates the follower to give a cash transfer to the leader having received the cash transfer the leader adopts a task division that compensates the contributions of the follower hence we observe a non cooperative gift exchange with a monetary gift to the leader and a subsequent non monetary reward to the follower through a lighter task allocation these gift exchanges disappear in the presence of infinitely many types of task divisions generated by a continuum of complementary tasks

effects of correlation on intermittent demand forecasting and stock control abstract this study investigates the effects of three different types of correlation on forecasting and stock control of intermittent demand items applying appropriate forecasting and stock control methods to theoretically generated compound poisson demand data we show that correlation in intermittent demand does play a role in forecast quality and stock control performance negative autocorrelation levels lead to higher service levels than positive values while cost does not significantly change our results also show that high intermittency levels intensify these changes in service level we also show that cross correlation produces results in the opposite direction of autocorrelation in size or intervals that is positive negative cross correlation leads to higher lower service levels

capacity precommitment as an entry barrier for price setting firms abstract for a bertrand edgeworth framework this paper considers whether investmentin capacity may serve as a barrier to entry when firms are identical except for the first mover precommitment possibilities that the incumbent enjoys subgame perfect nash equilibria are examined for a three stage non cooperative game in which the incumbent sets a capacity level the potential entrant chooses its capacity and then firms set prices using mixed strategies for some parameter values entry is blockaded positive profits for the entrant are precluded for other parameter values the incumbent may increase its capacity to prevent entry and maintain non negative profits

bertrand edgeworth oligopoly in large markets the relation between perfectly competitive and monopolistically competitive equilibria is analysed for a bertrand edgeworth model of a single market in which capacity constrained firms choose prices as strategies the market always has a nash equilibrium in pure or mixed strategies as the number of firms increases the corresponding equilibria converge in distribution to a perfectly competitive price this result provides a justification for perfect competition that is based on an explicit account of price formation however monopoly prices persist with a positive but vanishing probability regularity or well defined inverse demand functions are not required